/ 

A 

TEEATISE 

ON 

SURVEYING, 

CONTAINING 

THE THEORY AND PRACTICE: 

TO WHICH IS PREFIXED 

A PEKSPICUOUS SYSTEM 

OF 

PLANE TRIGONOMETRY. 

THE WHOLE CLEARLY DEMONSTRATED AND ILLUSTRATED BY A LARGE NUMBER 
OF APPROPRIATE EXAMPLES, 

PARTICULARLY ADAPTED TO THE USE OP SCHOOLS. 
BY JOHN "gUMMERE, A.M., 



FIFTEENTH EDITION, 

CAREFULLY REVISED, AND ENLARGED BY THE ADDITION OF ARTICLES ON THE 

THEODOLITE, LEVELLING, AND TOPOGRAPHY. 

ALSO, 

HINTS TO YOUNG SURVEYORS, 

BY A PRACTICAL SURVEYOR. 



PHILADELPHIA: 

URIAH HUNT & SON 

44 NORTH FOURTH STREET. 

1853. 




Entered, according to Act of Congress, in the year 1S53, by 

URIAH HUNT, 

in the Clerk's Office of the District Court of the United States in and for the Eastern 
District of Pennsylvania. 



TAW 



6-J&8 



CONTENTS. 



Logarithms ........ 9 

Geometrical Definitions . . ... . . 25 

Geometrical Problems ...... 29 

Plane Trigonometry ...... 37 

Application of Plane Trigonometry to the Mensuration of Distances 

and Heights ....... 70 

Practical Questions . . . . . . . .80 

Dimensions of a Survey ...... 83 

Supplying Omissions in the Dimensions of a Survey . . 109 

Problems for finding the Content of Land . . . 120 

Laying out and Dividing Land ..... 165 

Variation of the Compass •. . . . 205 

Miscellaneous Questions ...... 215 

Theodolite . . . . . . . 219 

Levelling ........ 239 

Topography ....... 257 

Hints to Young Surveyors . . ... 271 



PREFACE. 



The following compilation originated in the belief that our 
schools are in want of a Treatise on Surveying, adapted to the 
methods practised in this country, and freed from the defects of 
the systems now in use. Notwithstanding the importance of the 
science, and the large number that make it an object of study, it 
is believed we are not in possession of a treatise on this subject, 
suited to the wants of the student. The works of Gibson and 
Jess are the only ones at present in general use ; the former, 
though much the better of the two, is deficient in many respects. 
It may be sufficient here, merely to advert to its want of exam- 
ples, which renders it entirely unsuitable for a school book. From 
the latter, the student would in vain expect to become acquaint- 
ed with the principles of the science, or the rationale of any of 
the rules, necessary in performing the various calculations.* 

In order to understand the principles of surveying, a previous 
knowledge of Geometry is absolutely necessary; and this know- 
ledge will be best acquired from a regular treatise on the subject. 
In the demonstrations, therefore, throughout this work, the stu- 
dent is supposed to be acquainted with the elements of that 
science. The references are adapted to Playfair's Geometry 
but they will in general apply equally well to Simson's transla* 
tion of Euclid's Elements. 

As there are many who wish to obtain a practical knowledge 
of Surveying, whose leisure may be too limited to admit of their 

* Each of these works has lately gone through a new edition, in which consi- 
derable additions are stated to have been made. On examination, however, it 
does not appear, that those additions are such as to supply the deficiencies. 

The additions made to Gibson, consist principally of some nautical problems 
quite foreign to a treatise on Surveying. Those made to Jess, consist of a few 
extracts from Gibson, in one of which the Pennsylvania method of calculation is 
introduced, as being quite different from that given by Jess ; whereas it is well 
known to be the method given by that author, and used, as well in the preceding, 
as in the subsequent part of his work. 5 



going through a course of Geometry, the author has adapted his 
work to this class, by introducing the necessary geometrical defi- 
nitions and problems, and by giving plain and concise rules, en- 
tirely detached from the demonstrations ; the latter being placed 
in the form of notes at the bottom of the page. Each rule is ex- 
emplified by one wrought example ; and the most of them by 
several unwrought examples, with the answers annexed. 

In the laying out and dividing of land, which forms the most 
difficult part of surveying, a variety of problems is introduced, 
adapted to the cases most likely to occur in practice. This part 
of the subject, however, presents such a great variety of cases, 
that we should in vain attempt to give rules that would apply to 
all of them. It cannot therefore be too strongly recommended 
to every one, who has the opportunity, to make himself well ac- 
quainted with Geometry, and also with Algebra, previous to en- 
tering on the study of Surveying. Furnished with these useful 
auxiliaries, and acquainted with the principles of the science, the 
practitioner will be able to perform, with ease, any thing likely 
to occur in his practice. 

The compiler thinks proper to acknowledge, that in the ar- 
rangement of the work, he availed himself of the advice of his 
learned preceptor and friend, E. Lewis of New-Garden; and that 
several of the demonstrations were furnished by him. 



ADVERTISEMENT TO THE FOURTH EDITION. 



In preparing this edition for the press, several alter- 
ations have been made, which, it is believed, will be 
found to be real improvements. A number of new Pro- 
blems has been introduced, and a- more methodical 
arrangement of the whole has been adopted. Instead 
of three different rules for calculating the content of a 
Survey, one general rule, including these, is now given. 
It may be further added, that the rules for solving seve- 
ral of the problems in Division of Land, have been 
considerably simplified. The Mathematical Tables 
have been stereotyped, after carefully revising them and 
comparing them with the most correct European Edi- 
tions. THE AUTHOR. 



ADVERTISEMENT TO THE FOURTEENTH EDITION. 



To meet the wants of the Student of Civil Engi- 
neering, this edition has been enlarged by the addition 
of several chapters, in which the Theodolite and Le- 
velling Instrument are described, the methods of ad- 
justing and using them are given, and the principles 
and practice of Levelling and Topography are ex- 
plained and illustrated. — The whole has been carefully 
revised and the few typographical errors existing in 

former editions have been corrected. J. G. 

7 



CONTENTS. 



pao« 
Logarithms, -..-__._ 9 

Geometrical Definitions, ............... 25 

Geometrical Problems, -'---------------29 

Plane Trigonometry, 35 

Application of Plane Trigonometry to the Mensuration of Distances 

and Heights, 68 

Practical Questions, 78 

Dimensions of a Survey, ---------------81 

Supplying Omissions in the Dimensions of a Survey, ------107 

Problems for finding the Content of Land, 118 

Laying out and Dividing Land, ------------- 163 

Variation of the Compass, 202 

Miscellaneous Questions, --------------- 213 

Theodolite, 217 

Levelling, 237 

Topography, - 254 



EXPLANATION 

OF THE 

CHARACTERS USED IN THIS WORK. 

-{- signifies plus, or addition. 

— minus, or subtraction. 

X multiplication. 

-7- division. 

: :: : proportion. 

= equality. 

^ square root. 

0& difference between two quantities 

when it is not known which is the 

greater. 



TKEATISE ON SURVEYING. 



OF LOGARITHMS. 

Logarithms are a series of numbers so contrived, 
that by them the work of multiplication is performed 
by addition, and that of division by subtraction. 

If a series of numbers in arithmetical progression be 
placed as indices, or exponants, to a series of numbers 
in geometrical progression, the sum of difference of any 
two of the former, will answer to the product or quotient 
of the two corresponding terms of the latter. Thus, 

0. 1. 2. 3. 4. 5. 6. 7. &c, arith. series, or indices. 

1. 2. 4. 8. 16. 32. 64. 128. &c, geom. series. 

Now 2+3=5. also 7—3=4. 

And 4X8=32. and 128-5-8=16. 

Therefore the arithmetical series, or indices, have the 
same properties as logarithms ; and these properties 
hold true, whatever may be the ratio of the geometrical 
series. 

There may, therefore, be as many different systems of 
logarithms, as there can be taken different geometrical 
series having unity for the first term. But the most 
B 9 



10 OF LOGARITHMS. 

convenient system is that in which the ratio of the geome- 
trical series is 10; and this is the one in common use. 
Thus, 

0. 1 . 2. 3. 4. 5. &c. indices or logar. 

1. 10. 100. 1000. 10000. 100000. &c. natural numbers 

In this system the log. of 1. is 0,* the log. of 10 is 1. 
the log. of 100, is 2, &c. Hence it is plain that the log. 
of any number between 1 and 10, will be expressed by a 
decimal, the log. of any number between 10, and 100, by 1 
and a decimal, the log. of any number between 100 and 
1000, by 2 and a decimal, &c. 

The numbers, 0, 1, 2, 3, &c. that stand before the deci- 
mal part of logarithms, are called indices and are always 
less by unity, than the number of figures in the integral 
part of the corresponding natural number. 

The index of the logarithm of a number, consisting in 
whole, or in part of integers, is affirmative ; but if the 
number be a decimal, the index is negative, and is mark- 
ed by a negative sign ( — ) placed either before or above 
it. If the first significant figure of the decimal be ad- 
jacent to the decimal point, the index is, — 1, or \ ; if 
there be one cipher between them, the index is — 2, or 
2 ; if there be two ciphers between them, the index is — 3 
or 3, &c. 

The decimal parts of the logarithms of numbers, con- 
sisting of the same figures and in the same order, are the 
same, whether the number be integral, fractional, or 
mixed. This is illustrated as follows : 



* In every system the logarithm of 1 is 0. 



OF LOGARITHMS. 




Number 18960 


Logarithm 4.27784 


1896 




3.27784 


189.6 




2.27784 


18.96 




1.27784 


1.896 




0.27784 


.1896 




—1.27784 


.01896 




—2.27784 


.001896 




—3.27784 


.0001896 




—4.27784 



11 



The method of finding logarithms in the tables, and 
of multiplying, dividing, &c. by them, is contained in the 
following problems. 

PROBLEM I. 

To find the Logarithm of a given number. 

If the given number consists of one or two figures only, 
find it in the column marked No. in the first page of the. 
table, and against it, in the next column, marked log. is 
the logarithm. Thus the log. of 7 will be found 0.84510, 
and the log. of 85 will be found 1.92942. 

But if the given number be either wholly or in part 
decimal, the index must be changed accordingly. Ob- 
serving that the index must always be one less than the 
number of figures in the integral part of the given num- 
ber ; also, when the given number is wholly a decimal, 
the index is negative, and must be one more than the 
number of the ciphers between the decimal point and 
first significant figure on the left hand. Thus the log. 
of .7 is— 1.84510, and the log. of .0085 is —3.92942. 

If the given number consists of three figures, find it in 
one of the other pages of the table, in the column marked 
No. and against it, in the next column, is the decimal 



12 OF LOGARITHMS. 

part of the logarithm. The index must be placed before 
it agreeably to the above observation. Thus the log. 
of 421 is 2.62428, the log. of 4.21 is 0.62428, and the 
log. of .0421 is— 2.62428. 

If the given number consists of four figures, find the 
three left hand figures in the column marked No. as be- 
fore, and the remaining, or right hand figure at the top 
of the table ; in the column under this figure, and against 
the other three, is the decimal part of the logarithm. 
Thus the log. of 5163 is 3.71290, and the log. of .6387 
is— 1.80530. 

If the given number consist of five or six figures, find 
the logarithm of the four left hand figures as before ; 
then take the difference between this logarithm and the 
next greater in the table. Multiply this difference by 
the remaining figure or figures of the given number, and 
cut off one, or two figures to the right hand of the pro- 
duct, according as the multiplier consists of one, or two 
figures ; then add the remaining figure or figures of the 
product to the logarithm first taken out of the table, and 
the sum will be the logarithm required. Thus, let it be 
required to find the logarithm of 59686 ; then, 



Logarithm of 5968 is 
The next greater log. is 


- 


- 77583 

- 77590 


Difference 
Remaining figure 


7 
6 


Product - ' - 

To 

Add 


42 

- 77583 
4 



Decimal part of the log. - - 77587 



LOGARITHMS. 



13 



The natural number consisting of five integers, the in- 
dex must be 4 ; therefore the log. of 59686 is 4.77587. 

Again, let it be required to find the log. of .0131755 ; 
then, A 



Logarithm of 1317 is 
The next greater log. is 

Difference 
Remaining figures - 

Product 



11959 
11991 

32 
55 

1760 



To 

Add 



Decimal part of the log. 



- 11959 

18* 

- 11977 



As the given number is a decimal, and has one cipher 
between the decimal point and first significant figure, the 
index must be — 2; therefore the log. of .0131755 is 
—2.11977. 





E 


XAMPLES. 






1. 


Required the log. of 


4.3 


Ans. 


0.63347 


2. 


Required the log. of 


7986 


Ans. 


3.90233 


3. 


Required the log. of 


.3754 


Ans. 


-1.57449 


4. 


Required the log. of 


596.87 


Ans. 


2.77588 


5. 


Required the log. of 


785925 


Ans. 


5.89538 


6. 


Required the log. of 


6543900 


Ans. 


6.81583 


7. 


Required the log. of 


.0027863 


Ans. 


-3.44503 




* Because 17.6 is nearer 18 than 17. 





14 LOGARITHMS. 

PROBLEM II. 

To find the natural number corresponding to a given 
logarithm. 
If four figures only be required in the answer, look in 
the table for the decimal part of the given logarithm, 
and if it cannot be found exactly, take the one nearest 
to it, whether greater or less ; then the three figures in 
the first column, marked No. which are in a line with 
the logarithm found, together with the figure at the top 
of the table directly above it, will form the number re- 
quired. Observing, that when the index of the given 
logarithm is affirmative, the integers in the number 
found, must be one more than the number expressed by 
the index ; but when the index of the given logarithm is 
negative, the number found will be wholly a decimal, and 
must have one cypher less, placed between the decimal 
point and first significant figure on the left hand, than 
the number expressed by the index. Thus the natural 
number corresponding to the logarithm 2.90233 is 798.6, 
the natural number corresponding to the logarithm 
3.77055 is 5896, and the natural number corresponding 
to the logarithm —3.36361 is .00231. 

If the exact logarithm be found in the table, and the 
figures in the number corresponding do not exceed the 
index by one, annex ciphers to the right hand till they 
do. Thus the natural number corresponding to the lo- 
garithm 6.64068 is 4372000. 

If five or six figures be required in the answer, find, 
in the table, the logarithm next less than the given one, 
and take out the four figures answering to it as before. 
Subtract this logarithm from the next greater in the 
table, and also from the given logarithm ; to the latter 
difference, annex one or two ciphers, according as five 



LOGARITHMS. 15 

or six figures are required, and divide the number thus 
produced, by the former difference ; annex the quotient 
to the right hand of the four figures already found, and 
it will give the natural number required. 

Thus let it be required to find the natural number 
corresponding to the logarithm 2.53899 true to Jive 
figures ; then, 

Given logarithm - .53899 

Next less - - .53895 the natural number 

corresponding is 3459 

Diff. with one cipher annexed 40 

Next less log. - - .53895 
Next greater - - .53908 



Difference 13 

Divide 40 by 13 and the quotient will be 3, which, an- 
nexed to the right hand of 3459, the four figures already 
found, makes 34593 ;' therefore as the index is 2, the re- 
quired natural number is 345.93. 

Again let it be required to find the natural number 
corresponding to the logarithm 4.59859, true to six 
figures ,• then, 

Given logarithm - - .59859 

Next less - - .59857, the natural number an- 

swering to it is 3968. 

DifF. with two ciphers annexed 200 

Next less log. - - - 59857 

Next greater - - - 59868 



Difference - - - - 11 

Divide 200 by 11, and the quotient will be 18, which 
annexed to the right hand of 3968 the four figures al- 



1C LOGARITHMS. 

ready found, makes 396818; therefore as the index is 4, 
the required natural number is 39681.8. 

EXAMPLES. 

1. Required the natural number answering to the lo- 
garithm 1.88030. Ans. 75.91. 

2. Required the natural number answering to the lo- 
garithm 5.37081. Ans. 234861. 

3. Required the natural number answering to the lo- 
garithm 3.11977. Ans. 1317.56. 

4. Required the natural number answering to the lo- 
garithm— 2.97435. Ans. .094265. 

PROBLEM III. 

To multiply numbers by means of logarithms. 
Case 1. — When all the factors are whole or mixed 
numbers. 

RULE. 

Add together the logarithms of the factors, and the 
sum will be the logarithm of the product. 

EXAMPLES. 

1. Required the product of 84 by 56. 

Logarithm of 84 is 1.92428 

Do. of 56 is 1.74819 



Product 4704 Sum 3.67247 

2. Required the continued product of 17.3, 1.907 and 
34. 

Logarithm of 17.3 is 1.23805 
Do. 1.907 is 0.28035 

Do. 34. is 1.53148 



Product 1 1 21 .71 Sum 3.04988 



LOGARITHMS. 1? 

3. Find by logarithms the product of 76.5 by 5.5 
Ans. 420.75. 

4. Find by logarithms the continued product of 
42.35, 1.7364, and 1.76. Ans. 129.424. 

Case 2. — When some or all of the factors are decimal 
manners. 

BULB. 

Add the decimal parts of the logarithms as before, and 
if there be any to carry from the decimal part, add it to 
the affirmative index or indices, or else subtract it from 
the negative. 

Then add the indices together, when they are all of 
the same kind ; that is, all affirmative or all negative ; but 
when they are of different kinds, take the difference be- 
tween the sums of the affirmative and negative ones, and 
prefix the sign of the greater. 

Note. — When the index is affirmative, it is not neces- 
sary to place any sign before it ; but when it is negative, 
the sign must not be omitted. 

EXAMPLES. 

1. Required the continued product of 349.17, 25.43, 
93521 and .00576. 



Logarithm of 349.17 


is 


2.54303 


Do. 25.43 


is 


1.40535 


Do. .93521 


is 


-1.97090 


Do. .00576 


is 
Sum 


-3.76042 


Product 47.83 


1.67970 


3* C 







18 LOGARITHMS. 

In this example there is 2 to carry from the decimal 
part of the logarithms, which added to 3, the sum of 
the affirmative indices, makes 5; from this taking 4, 
the sum of the negative indices, the remainder is 1, 
which is the index of the sum of the logarithms, and is 
affirmative, because the sum of the affirmative indices, 
together with the number carried, exceed the sum of 
the negative indices. 

2. Required the continued product of .0839, .7536, 
and .003179. 

Logarithm of .0839 is -2.92376 
Do. .7536 is -1.87714 

Do. .003179 is -3.50229 



Product .000201 Sum -4.30319 

In this example there is 2 to carry from the decimal 
part of the logarithms, which subtracted from 6, the sum 
of the negative indices, leaves 4, which is the index of 
the sum of the logarithms, and is negative, because the 
sum of the negative indices is the greater. 

3. Required the continued product of 13.19, .3765, 
and .00415. Ana. .02061. 

4. Required the continued product of 343, 1.794, 
5.41, and .019. Ans. 63.25. 

PROBLEM IV. 

To divide numbers by means of Logarithms. 

Case 1. — When the dividend and divisor are both 
whole or mixed numbers. 



LOGARITHMS. 19 

RULE. 

From the logarithm of the dividend, subtract the lo- 
garithm of the divisor, the remainder will be the loga- 
rithm of the quotient. 

Note. — When the divisor exceeds the dividend, the 
question must be wrought by the rule given in the next 
case. 

EXAMPLES. 

1. Required the quotient of 3450 divided by 23. 

Logarithm of 3450 is 3.53782 
Do. 23 is 1.36173 



Quotient 150 Remainder 2.17609 

2. Required the quotient of 420.75 divided by 76.5. 

Ans, 5.5. 

3. Required the quotient of 37.1542 divided by 
1.73958. Ans. 21.3585. 

Case 2. — When the dividend or divisor, or both of 
them, are decimal numbers. 

rule. 

Subtract the decimal parts of the logarithms as before, 
and if 1 be borrowed in the left hand place of the deci- 
mal part, add it to the index of the divisor when that in- 
dex is affirmative, but subtract it when negative. 

Then conceive the sign of the index of the divisor 
changed from affirmative to negative, or from negative 
to affirmative ; and if, when changed, it be of the same 
name with that of the dividend, add the indices together 



20 LOGARITHMS. 

but if it be of a different name, take the difference of the 
indices, and prefix the sign of the greater. 

EXAMPLES. 

1. Required the quotient of .7591 divided by 32.147 

Logarithm of .7591 is -1.88030 
Do. 32.147 is 1.50714 



Quotient .02361 Remain. -2.37316 

In this example, the index of the divisor, with its sign 
changed, is — 1, which added to — 1, the index of the 
dividend, makes — 2, for the index of the quotient. 

2. Required the quotient of .63153 divided by .00917. 

Logarithm of .63153 is -1.80039 
Do. .00917 is -3.96237 



Quotient 68.8683 Remain. 1.83802. 

In this example there is 1 to carry from the decimal 
part of the logarithm, which subtracted from — 3, the 
index of the divisor, leaves — 2 ; this, with its sign 
changed, is-f-2; from which subtracting 1, the index of 
the dividend, the remainder is 1, and is affirmative, be- 
cause the affirmative index is the greater. 

3. Required the quotient of 13.921 divided by 7965.13. 

Logarithm of 13.921 is 1.14367 
Do. 7965.13 is 3.90125 



Quotient .001748 Remain. -3.24242 



LOGARITHMS. 21 

In this example there is 1 to carry from the decimal 
part of the logarithm, which added to 3, the index of 
the divisor, makes 4 ; this, with its sign changed, is, — 4 ; 
from which subtracting 1, the index of the dividend, the 
remainder is -—3. 

4. Required the quotient of 79.35 divided by .05178. 

Arts. 1532.46. 

5. Required the quotient of .5903 divided by .931. 

Ans. .63404. 

PROBLEM V. 

To involve a number to any power, that is, to find the square, 
cube, Sfc. of a number, logarithmically, 

RULE. 

Multiply the logarithm of the given number by the 
index of the power, viz. by 2 for the square, by 3 for the 
cube, &c. and the product will be the logarithm of the 
power. 

Note. — When the index of the logarithm is negative, 
if there be any to carry from the decimal part, instead 
of adding it to the product of the index and multiplier, 
subtract it, and the remainder will be the index of the 
logarithm of the power, and will always be negative. 

EXAMPLES. 

1. Required the square of 317. 

Logarithm of 317 is 2.50106 

2 



Square 100489 5.00212 



J LOGARITHMS. 

2. Required the 5th power of 1.735. 

Logarithm of 1.735 is 0.23930 

5 



5th power 15.7218 1.19650 
3. Required the cube of .08761. 

Logarithm of .08761 is -2.94255 

3 



Cube .0006724 -4.82765 

4. Required the cube of 7.503. Ans. 422.37. 

5. Required the 7th power of .32513. Ans. .0003841 . 

PROBLEM VI. 

To extract any root of a number logarithmically. 

RULE. 

Divide the logarithm of the given number by the index 
of the root, that is, by 2 for the square root, by 3 for the 
cube root, &c. and the quotient will be the logarithm of 
the required root. 

Note. — When the index of the logarithm is negative, 
and does not exactly contain the divisor, increase the 
index by a number just sufficient to make it exactly divi- 
sible by it, and carry the units borrowed, as so many 
tens, to the left hand figure of the decimal part ; then 
proceed with the division in the usual manner. 



LOGARITHMS. 23 

EXAMPLES. 



1. Required the cube root of 391.27. 

3) 
Logarithm of 391 .27 is 2.59248 



Cube root 7.314 0.86416 

2. Required the square root of .08593. 

Logarithm of .08593 is —2.93414 



Square root .29314 —1 46707 

3. Required the cube root of .7596. 

3) 
Logarithm of .7596 is —1.88058 



Cube root .9124 —1.96019 

4. Reouired the cube root of .0000613. 

3) 
Logarithm of .0000613 is— 5.78746 



Cube root .03943 —2.59582 

5. Required the square root of 365. Ans. 19.105. 

6. Required the 5th root of .9563. Ans. .9911. 

7. Required the 4th root of .00079. Ans. .16765 

Of the Arithmetical Complements of Logarithms. 

When it is required to subtract several logarithms 
from others, it will be more convenient to convert the 
subtraction into an addition, by writing down, instead 
of the logarithms to be subtracted, what each of them 
wants of 10.00000, which may readily be done, by writ- 



24 LOGARITHMS. 

ing down what the first figure, on the right hand, wants 
of 10, and what every other figure wants of 9; this re- 
mainder is called the Arithmetical Complement. Thus, if 
the logarithm be 2.53061, its arithmetical complement 
will be 7.46939. If one or more figures to the right 
hand be ciphers, write ciphers in their place, and take 
the first significant figure from 10, and the remaining 
figures from 9. Thus, if the logarithm be 4.61300, its 
arithmetical complement will be 5.38700. 

In any operation, where the arithmetical complements 
of logarithms are added to other logarithms, there must 
be as many tens subtracted from the sum, as there are 
arithmetical complements used. 

As an example, let it be required to divide the product 

of 76.4 and 35.84, by the product of 473.9 and 4.76. 

473.9 - - Ar. Co. 7.32431 

4.76 - - Ar. Co. 9.32239 

35.84 - - log. 1.55437 

76.4 - - log. 1.88309 



Quotient 1.214 0.08416 



GEOMETRY. 



DEFINITIONS. 

1. Geometry is that science wherein the properties 
of magnitude are considered. 

2. A point is that which has position, but not magni- 
tude. 

3. A line has length but not breadth. 

4. A straight, or right line, is the shortest line that 
can be drawn between any two points. 

5. A superficies or surface is that which has length and 
breadth, but not thickness. 

6. A plane superficies is that in which any two points 
being taken, the straight line which joins them lies 
wholly in that superficies. 

Fig. 1. 

7. A plane rectilineal angle is the incli- 
nation of two straight lines to one ano- 
ther, which meet together, but are not 
in the same straight line, as A, Fig. 1. a. 

Note. — When several angles are o 
formed about the same point, as at 
B, Fig. 2, each particular angle is 
expressed by three letters, whereof 
the middle letter shows the angu- 
lar point, and the other two the A 
lines that form the angle ; thus, CBD or DBC signifies 
the angle formed by the lines CB and DB. 

D 25 



Fig. 2. 




26 



GEOMETRY. 




8. The magnitude of an angle 
depends on the inclination which 
the lines that form it have to 
each other, and not on the length 
of those lines. Thus the angle 
DBE is greater than the angle ABC, Fig. 3. 

9. When a straight line stands on another straight 
line so as to incline to neither side, but 
makes the angles on each side equal, 
then each of those angles is called a 
right angle, and the line which stands 
on the other is said to be iicrpendicular 
to it. Thus ADC and BDC are right 

angles, and the line CD is perpendicular to AB, Fig. 4. 

10. An acute angle is that which is less than a right 
angle, as BDE, Fig. 4. 

11. An obtuse angle is that which is greater than a 
right angle, as ADE, Fig. 4. 

Fi &- 5 - 12. Parallel straight lines are those 

which are in the same plane, and 

A B which, being produced ever so far 

both ways, do not meet, as AB, CD, Fig. 5. 

13. A figure is a space bounded by one or more lines. 




Fig. 6. c 




14. A|i(«/e triangle is a figure bounded 
by three straight lines, as ABC, Fig. 6. 

Fig. 8. 15 A n equilateral triangle has 
A its three sides equal to each other, 
\ as A, Fig. 7. 

— ^ 16. An isosceles triangle has 



only two of its sides equal, as B, Fig. 



GEOMETRY. 



27 



17. A scalene triangle has three unequal sides, as 
ABC, Fig. 6. 

Fig. 9. C 

18. A right angled triangle has one right 
angle, as ABC, Fig. 9 ; in which the side 
AC, opposite to the right angle, is called 
the hypothenuse. 

19. An obtuse angled triangle has 
one obtuse angle, as C, Fig. 10. 




20. An acute angled triangle has all 
its angles acute, as ABC, Fig. 6. 

21. Acute and obtuse angled triangles are called 
oblique angled triangles. 

22. Any plane figure bounded by four right lines, is 
called a quadrilateral. 

23. Any quadrilateral, whose oppo- Fig, li. 
site sides are parallel, is called a joaral- I 
lelogram, as D, Fig. 11. (_ 



7 



J 



Fig. 12. 



Fig. 13. 



24. A parallelogram, whose angles are all 
right angles, is called a rectangle, as E, 
Fig. 12. 

25. A parallelogram whose sides are all 
equal, and angles right, is called a square, 
as F, Fig. 13. 

26. A rJwmboides is a parallelogram, whose 
opposite sides are equal, and angles oblique, as D, Fig. 11. 

27. A rhombus is a parallelogram, Fi s- u - 
whose sides are all equal and angles / / 
oblique, as G, Fig. 14. / G / 




28 



GEOMETRY. 



28. Any quadrilateral figure that is not a parallelo- 
gram, is called a trapezium. 

29. A trapezium that has two parallel sides is called 



Fig. 15. 



30. A right line joining any two opposite angles of a 
quadrilateral figure, is called a diagonal. 

31. That side upon which any parallelogram, or 
triangle is supposed to stand, is called the base; and 
the perpendicular falling thereon from the opposite 

angle is called the altitude of the 
parallelogram, or triangle. Thus 
AD is the base of the parallelogram 
ABEC, or triangle ABC, and CD is 
the altitude, Fig. 15. 

32. All plane figures contained under more than 
four sides, are called polygons ; of which those having 
five sides, are called pentagons ; those having six sides, 
Jiexagons, and so on. 

33. A regular polygon is one whose angles, as well 
as sides, are all equal. 




Fig. 16. 



34. A circle is a plane figure, bounded 
by one curve line called the circumfer- 
ence or periphery, every part of which 
is equally distant from a certain point 
within the circle; and this point is 
called the centre. Fig. 16. 



35. The radius of a circle is a straight line drawn 
from the centre to the circumference, as CB, Fig. 17. 

36. The diameter of a circle is a straight line drawn 
through the centre, and terminated both ways by the 




GEOMETRY. 29 

circumference, as AE, Fig. 17. It di- Fig B 17 ' 

vides the circle into two equal parts, 
called semicircles. 




37. A quadrant is one quarter of a 
circle, as ACB, Fig. 17. 

Note. — The fourth part of the cir- 
cumference of a circle is also called a quadrant. 

38. A segment of a circle is the figure contained by 
a right line, and the part of the circumference it cuts 
off: thus AEBA and AEDA are segments of the circle 
ABED, Fig. 16. 

39. An arc of a circle is any part of the circumfer- 
ence; as AD or DE, Fig. 17. 

40. Ratio is a mutual relation between two quantities 
of the same kind with respect to magnitude. 

Note. — A ratio is generally expressed, either by two 
numbers or by two right lines. 

41. When two quantities have the same ratio as two 
other quantities, the four quantities taken in order are 
called proportionals ; and the last is said to be a fourth 
proportional to the other three. 

42. When three quantities of the same kind are such 
that the first has to the second the same ratio which 
the second has to the third, the third is called a third 
proportional to the first and second, and the second is 
called a mean proportional between the first and third. 



30 



GEOMETRICAL PROBLEMS. 



GEOMETRICAL PROBLEMS. 



PROBLEM I. 



To bisect a right line, AB, Fig. 18. 

Fi e- 18 - Open the dividers to any dis- 

Xp/' tance more than half the line 

AB, and with one foot in A, 
describe the arc CFD ; with the 
same opening, and one foot in 
B, describe the arc CGD, meet- 
ing the first arc in C and D; 
from C to D draw the right line 
>&< CD, cutting AB in E, which will 

be equally distant from A and B. 



PROBLEM II. 

At a given point A, in a right line EF, to erect a per- 
pendicular, Fig. 19. 

Fig. 19. 

From the point A, lay off on 
each side, the equal distances AC, 
AD; from C and D, as centres, 
with any radius greater than AC 
or AD, describe two arcs intersect- 
ing each other in B ; from A to B, 
draw the line AB, which will be the perpendicular re- 
quired. 



GEOMETRICAL PROBLEMS. 



31 



PROBLEM III. 

To raise a perpendicular on t7ie end B of a right 
AB, Fig. 20. 



Fig. 20. 



\y 



/ 



Take any point D not in the 
line AB, and with the distance 
from D to B, describe a circle 
cutting AB in E; from E 
through D draw the right line 
EDO, cutting the periphery in A - 
C, and join CB, which will be 
perpendicular to AB. 



PROBLEM IV. 

To let fall a perpendicular upon a given line BC, from a 
given point A, without it, Fig. 21. 



In the line BC take any 
point D, and with it as a cen- 
tre and distance DA describe an 
arc AGE, cutting BC in G; 
with G as centre, and distance B 
GA, describe an arc cutting 
AGE in E, and from A to E 
draw the line AFE ; then AF 
will be perpendicular to AB. 



Fig. 21. 



■ / 



PROBLEM V. 

Through a given point A to draw 
a right line AB, parallel to a given 
tight line CD, Fig. 22. 

From the point A to any point c - 
F, in the line CD, draw the right 



a Fig. 22. 




61 GEOMETKICAL PROBLEMS. 

line AF ; with F as a centre and distance FA, describe 
the arc AE, and with the same distance and centre A 
describe the arc FG; make FB equal to AE, and 
through A and B draw the line AB, and it will be 
parallel to CD. 

PROBLEM VI. 

At a given point B, in a given rigid line LG, to make an 
angle equal to a given angle A, Fig. 23. 

Fig. 23. f With the centre A 

and any distance AE, 

describe the arc DE, 

and with the same 

distance and centre 

B describe the arc FG ; make HG equal to DE, and 

through B and H draw the line BH ; then will the 

angle HBG be equal to the angle A. 



PROBLEM VII. 

To bisect any rigid lined angle BAC, Fig. 24. 

Eig. 24. o In the lines AB and AC, from the 

point A, set off equal distances, AD 
and AE ; with the centres D and E 
and any distance more than half 
DE, describe two arcs cutting each 
other in F ; from A through F draw 
the line AG, and it will bisect the angle BAC. 





GEOMETRICAL PROBLEMS. 33 



PROBLEM VIII. 

To describe a triangle that s7iall Jiave its sides respect- 
ively equal to three right lines, D, E, and F, of which any 
two must be together greater than the third. Fig. 25. 

Make AB equal to D ; D J^ 25 - 

with the centre A and 
distance equal to E, de- 
describe an arc, and with 

the centre B and distance equal to F describe another 
arc, cutting the former in C ; draw AC and BC, and 
ABC is the triangle required. 

PROBLEM IX. 

Upon a given line AB to describe a square, Fig. 26. 

At the end B of the line AB, by Problem 
III. erect the perpendicular BC, and make 
it equal to AB ; with A and C as centres, 
and distance AB or BC, describe two arcs 
cutting each other in D ; draw AD, and 
CD, then will ABCD be the square required. 

PROBLEM X. 

To describe a circle that shall pass through the angidar 




HW7 

points A, B, and C, of a triangle ABC, Fig. 27. 



By Problem I. bisect any two of cFig^27- 

the sides, as AC, BC, by the perpen- D 
diculars DE and FG ; the point H 
where they intersect each other will 
be the centre of the circle: with 
this centre, and the distance from 
E 




34 



GEOMETRICAL PROBLEMS. 




it to either of the points A, B, or C, describe the 
circle. 

PROBLEM XI. 

To divide a given right line AB into any number of 
equal parts, Fig. 28. 

Draw the indefinite right line 
AP, making an angle with AB, 
also draw BQ, parallel to AP, in 
each of which, take as many equal 
parts AM, MN, &c. Bo, on, &c, as 
the line AB is to be divided into ; 

then draw Mm, Nn, &c, intersecting AB in E, F, &c, 

which will divide the line as required. 

PROBLEM XII. 

To make a plane diagonal scale, Fig. 29. 

Draw eleven lines parallel to, and equidistant from 
each other ; cut them at right angles by the equidistant 
lines BC; EF; 1, 9; 2, 7; &c. then will BC, &c. be 
divided into ten equal parts ; divide the lines EB, and 
FC, each into ten equal parts ; and from the points of 
division on the line EB, draw diagonals to the points 
of division on the line FC : thus join E and the first 
division on FC, the first division on EB, and the second 
on FC, &c. 



I 


5 


4 


Fig. 29. 
i 


i ] 


] 


E 2 4 


6 S V 








1 1 1-1 










i In 


L 










1 1 i 


\\ - 














TT i 


--±tu 














U-J- 


t 4-F 














■ 1 


l±±i-, 














■ 1 :1 ' 














11 - M 9 






1 






\\\U if 






1 




1 1 UU.1 11 In 



Note. — Diagonal scales serve to take off dimensions 
or numbers of three figures. If the first large divisions 
be units, the second set of divisions, along EB, will be 



GEOMETRICAL PROBLEMS. 



35 



10th parts , and the divisions in the altitude, along BC, 
will be 100th parts. If HE be tens, EB, will be units, 
and BC will be tenth parts. If HE be hundreds, BE will 
be tens, and BC units. And so on, each set of divisions 
being tenth parts of the former ones. 

For example, suppose it were required to take off 242 
from the scale. Extend the dividers from E to 2 towards 
Hj and with one leg fixed in the point 2, extend the other 
till it reaches 4 in the line EB ; move one leg of the di- 
viders along the line 2, 7, and the other along the line 4, 
till they come to the line marked 2, in the line BC, and 
that will give the extent required. 

PROBLEM XIII. 

To find a third proportional to two given right lines. 
A and B. 

Draw two right lines, CD, CE B 
containing any angle ; make CF a 
equal A, and CG,CH, each equal 
B ; join FG and draw HL paral- 
lel to it: then will CL be the third 
proportional required. 

PROBLEM XIV. 

To find a fourth proportional to three given right lines, 
A, B and C. 




Draw two right lines, DE, DF B ' 
containing any angle ; make DG c ' 
equal A, DH equal B, and DL 
equal C ; join GH and draw LM 
parallel to it: DM will be a 
fourth proportional to A, B, 
andC. 



E 




HM 



36 



GEOMETRICAL PROBLEMS. 



PROBLEM XV. 

To find a mean proportional between two given right lines 
A and B. 



Draw any right line CE and in 
it take CD equal A, and DE equal 
B; bisect CE in F, and with the 
centre F and radius FC or FE 
describe the semicircle CGE ; 
draw DG perpendicular to CE : 
then DG will be a mean propor- 
tional between A and B. 




PROBLEM XVI. 

To divide a given right line AB into two parts that 
shall have the same ratio to each other as two given lines C 
and D. 



Draw AE making an angle 
with AB ; in AE take AF equal ^ 
C and FE equal D : join EB and 
draw FG parallel to it ; then AG 
will have to GB the same ratio A 
that C has to D. 




PROBLEM XVII. 

To divide a given right line AB in two parts in the point 
D, so that AD may he to DB in the ratio of two given num- 
bers m and n. For example, let m=3, and ?i=4. 



Draw AC making any angle with AB ; take 
the number m from any convenient scale 
of equal parts, and lay it on AC, from A to E ; 
and take the number n from the same scale, 
and lay it from E to C ; join CB and draw ED 
parallel to it ; then AB will be divided as re- 
quired. 




PLANE TRIGONOMETRY. 



DEFINITIONS. 




1. Plane Trigonometry is the art by which, when 
any three parts of a plane triangle, except the three 
angles, are given, the others are determined. 

2. The periphery of every circle is supposed to be 
divided into 360 equal parts, called degrees; each 
degree into 60 equal parts, called minutes ; and each 
minute into 60 equal parts, called seconds, &c. 

3. The measure of an angle is the 
arc of a circle, contained between the 
two lines that form the angle, the an- 
gular point being the centre ; thus the 
angle ABC, Fig. 30, is measured by the arc DE, and 
contains the same number of degrees that the arc does. 
The measure of a right angle is therefore 90 degrees; 
for DH, Fig. 31, which measures the right angle DCH, 
is one-fourth part of the circumference, or 90 degrees. 

Note. — The degrees, minutes, seconds, &c, contamed 
in any arc, or angle, are written in this manner, 50° 
18' 35"; which' signifies that the given arc or angle 
contains 50 degrees, 18 minutes, and 35 seconds. 

4. The aymplement of an arc, or of an angle, is what 
it wants of 90°; and the supplement of an arc, or of 
an angle, is what it wants of 180°. 

5. The clwrd of an arc, is a right line drawn from 
one extremity of the arc to the other : thus the line 
BE is the chord of the arc BAE or BDE, Fig. 31. 

37 



38 



PLANE TRIGONOMETRY. 



Fig. 31 




6. The sine of an arc, is a right 
line drawn from one extremity of 
the arc perpendicular to the dia- 
meter which passes through the 
other extremity : thus BF is the 
sine of the arc AB or BD, Fisr. 31. 



7. The cosine of an arc, is that 
part of the diameter which is in- 
tercepted between the sine and the centre : thus CF is 
the cosine of the arc AB, and is equal to BI, the sine 
of its complement HB, Fig. 31 

8. The versed sine of an arc, is that part of the diameter 
which is intercepted between the sine and the arc : thus 
AF is the versed sine of AB; and DF of DB, Fig. 31. 

9. The tangent of an arc, is a right line touching the 
circle in one end of the arc, being perpendicular to the 
diameter which passes through that end, and is termi- 
nated by a right line drawn from the centre through the 
other end : thus AG is the tangent of the arc AB, Fig. 31. 

10. The secant of an arc, is the right line drawn from 
the centre and terminating the tangent ; thus CG is the 
secant of AB, Fig. 31. 

11. The cotangent of an arc, is the tangent of the 
complement of that arc ; thus HK is the cotangent of 
AB, Fig. 31. 

12. The cosecant of an arc, is the secant of the com- 
plement of that arc ; thus CK is the cosecant of AB, 
Fig. 31. 

13. The sine, cosine, &c, of an angle is the same as 
the sine, cosine, &c, of the arc that measures the 
angle. 



PLANE TRIGONOMETRY. 



39 



--/. 



PROBLEM I. F 

To construct the lines of cords, 
angents, and secants, to any 
radius. Fig. 32. 

Describe a semicircle with any 
convenient radius CB; from the 
centre C draw CD perpendicular 
to AB, and produce it to F ; draw 
BE parallel to CF and join AD. 

Divide the arc AD into nine eo 
equal parts, as A 10 ; 10, 20, &c, 
and with one foot of the dividers 5 o 
in A, transfer the distances A, 10; 
A, 20, &c, to the right line AD ; 
then will AD be a 
line of chords con- 
structed to every 
ten degrees. 

Divide BD into 
nine equal parts, 
and from the points 
of division, 10, 20, 30, &c, draw lines parallel to CB,* 
and meeting CD in 10, 20, 30, &c, and CD will be a 
line of sines. 

From the centre C, through the divisions of the arc 
BD, draw lines meeting BE, in 10, 20, 30, &c, and 
BE will be a line of tangents. 

With one foot of the dividers in C transfer the dis- 
tances from C to 10, 20, &c, in the line BE to the line 
CF, which will then be a line of secants. 

* To avoid confusion, these lines are not drawn in the figure. 




40 PLANE TRIGONOMETRY. 

By dividing the arcs AD and BD each into 90 equal 
parts, and proceeding as above, the lines of chords, 
sines, &c, may be construed to every degree of the 
quadrant. 

PROBLEM II. 

At a given point A in a given right line AB, to make 
an angle of any proposed number of degrees, suppose 38 
degrees. Fig. 33. 

Fig. 33. ^ With the centre A, and a radius 
equal to 60 degrees, taken from a scale 
of chords, describe an arc, cutting AB 
in m ; from the same scale of chords, 
take 38 degrees and apply it to the 
arc from m to n, and from A through 

n draw the line AC ; then will the angle A contain 38 

degrees. 

Note. — Angles of more than 90 degrees are taken off 
at twice. 

PROBLEM III. 

To measure a given angle A. Fig. 34. 

Fig. 34. Describe the arc mn with the chord 

of 60 degrees, as in the last problem. 
Take the arc mn between the dividers, 
and that extent applied to the scale of 
chords will show the degrees in the 
given angle. 

iVbfe. — When the distance mn exceeds 90 degrees, it 
must be taken off at twice, as before. 




PLANE TRIGONOMETRY. 41 

OF THE TABLE 

OF 

LOGARITHMIC OR ARTIFICIAL SINES, TANGENTS, &c. 



This table contains the logarithms of the sine, tan- 
gent, &c. to every degree and minute of the quadrant, 
the radius being 10000000000, and consequently its lo- 
garithm 10. 

Let the radius CB, Fig. 32, be supposed to consist of 
10000000000 equal parts as above, and let the qua- 
drant DB be divided into 5400 equal arcs, each of these 
will therefore contain 1'; and if from the several points 
of division in the quadrant, right lines be drawn perpen- 
dicular to CB, the sine of every minute of the quadrant 
to the radius CB will be exhibited. The lengths of these 
lines being computed and arranged in a table, constitute 
what is usually termed a table of natural sines. The 
logarithms of those numbers taken from a table of loga- 
rithms, and properly arranged, form the table of loga- 
rithmic or artificial sines. In like manner the logarithmic 
tangents and secants are to be understood. 

The method by which the sines are computed is too 
abstruse to be explained in this work, but a familiar ex- 
position of this subject, as well as of the construction of 
logarithms may be seen in Simpson's trigonometry. 

To find, by the table, the sine, tangent, fyc. of an arc or 
angle. 

If the degrees in the given angle be less than 45, look 

for them at the top of the table, and for the minutes, in 
4* F 



42 PLANE TRIGONOMETRY. 

the left hand column ; then in the column marked at the 
top of the table, sine, tangent, &c. and against the mi- 
nutes, is the sine, tangent, &c. required. If the degrees 
are more than 45, look for them at the bottom of the 
table, and for the minutes, in the right hand column ; 
then in the column marked at the bottom of the table, 
sine, tangent, &c. and against the minutes, is the sine, 
tangent, &c. required. 

Note. — The sine of an angle and of its supplement 
being the same, if the given number of degrees be above 
90, subtract them from 180°, and find the sine of the re- 
mainder. 

EXAMPLES. 

1. Required the sine of 32° 27' Ans. 9.72962. 

2. Required the tangent of 57° 39' Ans. 10.19832. 

3. What is the secant of 89° 31' Ans. 12.07388. 

4. What is the sine of 157° 43' Ans. 9.57885. 

To find the degrees and minutes corresponding to a given 
sme, tangent, &c. 

Find, in the table, the nearest logarithm to the given 
one, and the degrees answering to it will be found at 
the top of the table, if the name be there, and the mi- 
nutes on the left hand ; but if the name be at the bottom 
of the table, the degrees must be found at the bottom, 
and the minutes at the right hand. 

EXAMPLES. 

1. Required the degrees and minutes in the angle 
whose sine is 9.64390. Ans. 26° 8. 



PLAJtfE TRIGONOMETRY. 43 

2. Required the degrees and minutes in the angle 
whose tangent is 10.47464. Arts. 71° 28'. 



ON GUNTER'S SCALE. 

Gunter's scale is an instrument by which, with a pair 
of dividers, the different cases in trigonometry, and many 
other problems, may be approximately solved. 

It has on one side, a diagonal scale, and also the lines 
of chords, sines, tangents, and secants, with several 
others. 

On the other side there are several logarithmic lines 
as follow : 

The line of numbers marked Num., is numbered from 
the left hand of the scale towards the right, with 1, 2, 3, 
4, 5, 6, 7, 8, 9, 1, which stands in the middle of the 
scale ; the numbers then go on 2, 3, 4, 5, 6, 7, 8, 9, 10, 
which stands at the right hand end of the scale. These 
two equal parts of the scale are similarly divided, the 
distances between the first 1, and the numbers 2, 3, 4, 
&c. being equal to the distances between the middle 1, 
and the numbers 2, 3, 4, &c. which follow it. The sub- 
divisions of the two parts of this line are likewise simi- 
lar, each primary division being divided into ten parts, 
distinguished by lines of about half the length of the pri- 
mary divisions. 

The primary divisions on the second part of the scale, 
are estimated according to the value set upon the unit on 
the left hand of the scale. If the first 1 be considered 
as a unit, then the first 1, 2, 3, &c. stand for 1,2, 3, &c 
the middle 1 is 10, and the 2, 3, 4, &c. following stand 



44 PLANE TRIGONOMETRY. 

for 20, 30, 40, &c. and the ten at the right hand for 100. 
If the first 1 stand for 10, the first 2, 3, 4, &c. must be 
counted 20, 30, 40, &c. the middle 1 will be 100, the 
second 2,3, 4, &c.will stand for 200, 300, 400, &c. and 
the 10 at the right hand for 1000. 

If the first 1 be considered as tV of a unit, the 2, 3, 4, 
&c. following will be -h, fV, tV, &c. and the middle 1, 
and the 2, 3, 4, &c. following, will stand for 1, 2, 3, 4, &C 

The intermediate small divisions must be estimated 
according to the value set upon the primary divisions. 

Si?ies. — The line of sines, marked Sin., is numbered 
from the left hand of the scale towards the right, 1, 2, 3, 
4, &c. to 10, then 20, 30, 40, &c. to 90, where it termi- 
nates just opposite 10 on the line of numbers. 

Tangents. — The line of tangents, marked Tan., begins 
at the left hand, and is numbered 1, 2, 3, &c. to 10, then 
20, 30, 40, 45, where there is a brass pin, just under 90 
in the line of sines ; because the sine of 90° is equal to 
the tangent of 45°. From 45 it is numbered towards the 
left hand 50, 60, 70, 80, &c. The tangent arcs of above 
45° are therefore counted backward on the line, and are 
found at the same points of the line as the tangents of 
their complements. 

There are several other lines on this side of the scale, 
as Sine Rhumbs, Tangent Rhumbs, Versed Sines, die. ; 
but those described are sufficient for solving all the pro- 
blems in plane trigonometry. 

Remarks on Angles, Triangles, Sfc. 

1. If from a point D in a right line AB, one or more 
right lines be drawn on the same side of it, the angles 
thus formed at the point D will be together equal to two 



PLANE TRIGONOMETRY. 



45 




Fig. 36. 



right angles, or 180° ; thus ADE 
-f EDB= two right angles, or 180°: 
also ADC + CDE + EDB = two 
right angles, or 180°. Fig. 35. 

2. Since the angles thus formed A 
at the point D, on the other side 

of AB, would also be equal to two right angles, the 
sum of all the angles formed about a point is equal to 
four right angles, or 360°. 

3. If two right lines cut one ano- c 
ther, the opposite angles will be 
equal: thus AEC=BED, and AED 
= CEB, Fig. 36. 

4. The sum of the three angles of 
a plane triangle is equal to two rightangles, or 180°. 

5. If the sum of two angles of a triangle be sub- 
tracted from 180°, the remainder will be the third 
angle. 

6. If one angle of a triangle be subtracted from 180°, 
the remainder will be the sum of the other two angles. 

7. In rightrangled triangles, if one of the acute angles 
be subtracted from 90°, the remainder will be the other 
acute angle. 

8. The angles at the base of an isosceles triangle 
are equal to one another. 

9. If one side of a triangle be pro- 
duced, the external angle will be 
equal to the sum of the two exter- 
nal and opposite angles : thus the 
external angle CBD, of the triangle 

ABC, is equal to the sum of the internal and opposite 
angles A and C, Fig. 37. 




46 



PLANE TRIGONOMETRY. 



10. The angle at the centre of a 
circle is double of the angle at the 
circumference, upon the same base, 
that is upon the same part of the 
circumference : thus the angle BEC 
is double of the angle BAC, Fig. 38. 

11. The angles in the same seg- 
ment of a circle are equal to one 
another: thus the angle BAD is 
equal to the angle BED ; also the 
angle BCD is equal to the angle 
BFD, Fig. 39. 

12. The angle in a semicircle is a 
right angle: thus the angle ECF, 
Fig. 45, is a right angle. 

13. This mark ' placed on the sides or in the angles 
of a triangle, indicates that they are given ; and this 
mark ° placed in the same way, indicates that they are 
required. 




PRACTICAL RULES FOR SOLVING ALL THE CASES 
OF PLANE TRIGONOMETRY. 

CASE 1. 

The angles and one side of any plane triangle being given, 
to find the otlier sides. 

RULE. 

As the sine of the angle opposite the given side, 
Is to the sine of the angle opposite the required side, 
So is the given side, 
To the required side.* 

* Demonstration. Let ABC, Fig 40, be any plane triangle ; take BF= 
AC, and upon AB let fall the perpendiculars CD and FE, -which will be 



PLANE TRIGONOMETRY. 47 

Note 1. — The proportions in trigonometry are worked 
by logarithms : thus, from the sum of the logarithm of 
the second and third terms, subtract the logarithms of 
the first term, and the remainder will be the logarithm 
of the fourth term. 

2. The logarithmic sine of a right angle or 90° is 
10.00000, being the same as the logarithm of the 
radius. 

EXAMPLES. 

1. In the triangle ABC, there are given the angle A 
= 32° 15', the angle B=114° 24', and consequently the 
angle C = 33° 21', and the sides AB=98 ;* required the 
sides AC and BC. 



By Construction, Fig. 41. 

Make AB equal to 98 by a scale of Fi s- 41 - 

equal parts, and draw AC, making 
the angle A =32° 15'; also make the 
angle B = 114° 24', and produce BC, 
AC, till they meet in C, then is ABC 
the triangle required ; and AC measured by the same 
scale of equal parts, is 162, and BC is 95. 

the sines of the angles A and B to the equal C Fig- 40. 

radii AC and BF. Now the triangles BDC 

and BEF being similar, we have CD : FE : : 

BC : BF : or AC ; that is sin. A : sin. B : : 

BC : AC. In like manner it is proved, that 

sin. A : sin. C : : BC : AB. When one of the 

angles is obtuse, the demonstration is the same. Hence it appears, that 

in any plane triangle, the sides are to one another as the sines of their 

opposite angles. 

* This 98 may express so many feet, or yards, &c, and the other sides 
will be of the same denomination as the given. 





48 PLANE TRIGONOMETRY. 

By Calculation. 
AssineoftheangleC33°21' - - 9.74017 

Is to sine of the angle B 114° 24' - - 9.95937 
So is AB 98 1.99123 

11.95060 
9.74017 

To AC 162.3 2.21043 

As sine of C 33° 21' - - - - 9.74017 

Is to sine of A 32° 15'- - - - 9.72723 
So is AB 98 1.99123 

11.71846 
9.74017 

To BC 95.12 1.97829 

By Gunter's Scale. 

Extend the compasses, on the line of sines, from 
33° 21' to 65° 36' the supplement of the angle B ; that 
extent will reach, on the line of numbers, from 98 to 162, 
the side AC. 

Extend the compasses from 33' 21' to 32° 15' on the 
line of sines ; that extent will rea< h, on the line of num 
bers, from 98 to 95, the side BC. 

2. In the right-angled triangle ABC, are given the 
hypothenuse AC=480, and the angle A=53° 8'. To 
find the base AB and perpendicular BC. 



PLANE TRIGONOMETRY. 49 

From 90° subtract the angle A=53° 8'; the remain- 
der 36° 52' will be the angle C. The angle B, being a 
right angle, is 90°. 

By Construction, Fig. 42. 

This may be constructed as in the preced- Fi s- 42, ° 
ing example, or otherwise thus, 

Draw the line AB of any length, and draw 
AC, making the angle A =53° 8'; make AC 
= 480 by a scale of equal parts, and from C 
draw CB perpendicular to AB, then ABC is 
the triangle required. AB measured by the same scale 
of equal parts, will be 288, and BC will be 384. 

By Calculation. 
As sine of B 90 10.00000 




Is to sine of A 53° 8' - - - - 9.90311 
So is AC 480 2.68124 



12.58435 



ToBC384 2.58435 

As sine of B 90° - - - - - - 10.00000 



Is to sine of C 36° 52' - - - - 9.77812 
So is AC 480 2.68124 



12.45936 



ToAB288 2.45936 

G 



50 PLANE TRIGONOMETRY. 



By Gunters Scale. 

Extend the compasses, on the line of sines, from 90° 
to 53° 8', that extent will reach, on the line of numbers, 
from 480 to 384, the perpendicular BC. 

Extend the compasses, on the line of sines, from 90° 
to 36° 52', the complement of the angle A; that extent 
will reach, on the line of numbers, from 480 to 288, the 
base AB. 

3. In the triangle ABC, are given the angle A=79° 
23', the angle B=54° 22', and the side BC=125; re- 
quired AC and AB. Ans. AC=103.4, and AB=91.87. 

4. In a right-angled triangle, there are given the 
angle A=56° 48', and the base AB=53.66, to find the 
perpendicular BC and hypothenuse AC. Ans. BC=82 
and AC=98. 

5. In the right-angled triangle ABC, are given the 
angle A=39° 10', and the perpendicular BC=407.37, to 
find the base AB and hypothenuse AC. Ans. AB=500.1, 
and AC=645. 

CASE 2. 

Two sides and an angle opposite one of them being given, 
to find the other angles and side. 

RULE. 

As the side opposite the given angle, 

Is to the other given side, 

So is the sine of the angle opposite the former, 

To the sine of the angle opposite the latter.* 

* This is evident from the demonstration of the rule in the preceding case. 



PLANE TRIGONOMETRY. 51 

Add the angle thus found to the given angle, and 
subtract their sum from 180°, the remainder will be 
the third angle. 

After finding the angles, the other side may be found 
by Case 1. 

Note. — The angle found by this rule is sometimes 
ambiguous ; for the operation only gives the sine 
of the angle, not the angle itself; and the sine of 
every angle is also the sine of its supplement. 

When the side opposite the given angle is equal to, 
or greater than the other given side, then the angle 
opposite that other given side is always acute; but 
when this is not the case, that angle may be either 
acute or obtuse, and is consequently ambiguous. 

EXAMPLES. 

1. In the triangle ABC, are given the angle C = 33° 
21', the side AB = .98 and the side BC = .7912; re- 
quired the angles A and B, and the side BC. 

By Construction, Fig. 43. 

Make BC = .7912 by a scale J^- 43. 

of equal parts, and draw CA, .-AjT" """"""N. 

making the angle C= 33° 21'; /' v\ 
with the side AB = .98, in the \ >v \ 

compasses, taken from the same \ ^O \ 

scale of equal parts, and B as B j 

a centre, describe the arc ab, 

cutting AC in the point A, and join BA ; then is ABC the 
triangle required : the side AC, measured by the scale of 
equal parts, will be 1.54, and the angles A and B, mea- 
sured by a scale of chords, will be 26° 21' and 120° 18'. 

Here the arc ab cuts AC in one point only, because 
AB is greater than BC ; therefore the angle A is acute, 
and not ambiguous. 



52 PLANE TRIGONOMETRY. 

By Calculation. 
AsAB,.98 —1.99123 



Is to BC, .7912 —1.89829 

So is sine ofC, 33° 21' - - - 9.74017 



9.63846 



To sine of A, 26° 21' - - 9.64723 

To the angle C=33° 21' add the angle A=26° 21' and 
the sum is 59° 42' which subtracted from 180° leaves 
the angle B= 120° 18' 

As sine of C, 33° 21' - - - - 9.74017 



Is to sine of B, 120° IS*. 9.93621 

So is AB, .98 .... —1.99123 



9.92744 



To AC, 1.539 ... - 0.18727 

By Guttler's Scale. 

Extend the compasses from .98 to .79 on the line of 
numbers, that extent will reach from 33° 21' to 26° 21', 
the angle A, on the line of sines. 

Add the angle A=26° 21' to the angle C=33° 21', 
and the sum will be 59° 42'; then extend the compasses 
from 33° 21' to 59° 42', on the line of sines, that extent 
will reach from .98 to 1.54, the side AC, on the line of 
numbers. 

2. In the triangle ABC, are given the angle C=33° 21', 
the side BC=95.12 and the side AB=60, to find the 
angles A and B, and the side AC. 



PLANE TRIGONOMETRY. 53 

By Construction, Fig. 44. 

This is constructed in the same Fi s- 44 - 

manner as the preceding exam- a 
pie ; only, AB being shorter than " 
BC, the arc ah cuts AC in two 
points on the same side of BC ; 
hence the angle A may be either 
acute or obtuse. The side required has also two values, 
as AC and AC. 

By Calculation. 
As AB, 60 1.77815 




Is to BC, 95.12 1.97827 

So is sine C, 33° 21' 9.74017 



11.71844 



TosineofAptf-*} 9.94029 

The sum of the angles C and A subtracted from 180° 
leaves the angle B=86° 1' if A be acute, or 27° 17' if 
A be obtuse. 

To find the side AC answering to the acute value of 
the angle A. 

As sine of C, 33° 21' - - - - 9.74017 

Is to sine of B, 86° 1' - - - - 9.99895 
So is AB, 60 1.77815 

11.77710 



To AC, 108.9 2.03693 

To find the side AC, answering to the obtuse value 
of the angle A. 



54 



PLANE TRIGONOMETRY. 

AssineofC,33°21' - - - 9.74017 


Is to sine of B, 27° 17 - 
SoisAB,60 - - - - 


- - 9.66124 
1.77815 




11.43939 


ToAC,50.03 .... 


- 1.69922 



3. In a triangle ABC, the side AB is 274, AC 306. 
and the angle B 78° 13'; required the angles A and C. 
and the side BC. 

Ans. A=40° 33', C=61° 14', andBC=203.2. 

4. In a right-angled triangle, there are given the 
hypothenuse AC=272, and the base AB=232; to find the 
angles A and C, and the perpendicular BC. 

Ans. A=31° 28' C=58° 32* and BC=142. 

5. In a right-angled triangle ABC, the hypothenuse 
AC is 150, and one sideBC 69; required the angles and 
other side. 

Ans. C=62° 37', A=27° 23', and AB 133.2. 

CASE 3. 

Two sides and the included angle being given, to find the 
other angles and side. 

RULE. 

Subtract the given angle from 180°, and the remainder 
will be the sum of the two unknown angles. Then, 
As the sum of the two given sides, 
Is to their difference ; 



PLANE TRIGONOMETRY. 55 

So" is the tangent of half the sum of the two un- 
known angles, 
To the tangent of half their difference.* 
This half difference of the two unknown angles, 
added to their half sum, will give the angle opposite 
the greater of the two given sides, and being subtracted 

* Demonstration. Let ABC, Fig. 45, be the Fig. 45. 

proposed triangle, having the two given sides 
AB, AC, including the given angle A. About 
A as a centre, with AC the greater of the given 
sides for a radius, describe a circle meeting AB 
produced in E and F, and BC in D ; join DA, 
EC, and FC, and draw FG parallel to BC, meet- 
ing EC produced in G. 

The angle EAC (32.1.) is equal to the sum of 
the unknown angles ABC, ACB ; and the angle EFC at the circumference, 
is equal to the half of EAC at the centre (20.3. ;) therefore EFC is half 
the sum of the unknown angles ; but (32.1.) the angle ABC is equal to 
the sum of the angles BAD and ADB, or BAD and ACB ; therefore FAD 
is the difference of the unknown angles ABC, ACB ; and FCD, at the cir- 
cumference is the half of that difference ; but because of the parallels 
DC, FG, the angles GFC, FCD are equal ; therefore GFC is equal to half 
the difference of the unknown angles ABC, ACB ; but since the angle 
ECF in a semicircle, is a right angle, EG is perpendicular to CF, and 
therefore CF being radius, EC, CG are the tangents of the angles EFC, 
CFG ; it is also evident that EB is the sum of the sides BA, AC, and that 
BF is the difference ; therefore since BC, FG are parallel, EB : BF : : 
EC : CG (2.6. :) that is, the sum of the sides AC, AB, is to their difference, 
as the tangent of half the sum of the angles ABC, ACB, is to the tangent 
of half their difference. 

To demonstrate the latter part of the Fig. 46. 
rule, let AC and AB, Fig. 46, represent c E B d 




any two magnitudes whatever ; in AB pro- 
duced, take BD equal to AC the less, and bisect AD in E. 

Then because AE is equal to ED, and AC to BD, CE is equal to EB ; 
therefore AE or ED is half the sum of the given magnitudes AB, AC, 
and CE, or EB is half their difference ; but AB the greater is equal to 
AE, EB, that is to half the sum added to half the difference ; and AC the 
less, is equal to the excess of AE, half the sum, above CE, half the dif- 
ference. 



56 



PLANE TRIGONOMETRY. 



from the half sum will give the angle opposite the less 
given side. 

After finding the angles, the other side may be found 
by Case 1. 



EXAMPLES. 



1. In the triangle ABC, there are given AB = 128, 
AC = 90, and the angle A =48° 12', to find the angles 
B and C, and the side BC. 



By Construction, Fig. 47. 

Draw AB = 128, and make the 
angle A = 48° 12'; draw AC=90, 
and join BC. The angle B will 
measure 44° 37', the angle C 87° 
11', and the side BC 95.5. 




AB 

AC 



128 
90 



By Calculation. 



Angle A 



180° 0' 
48 12 



Sum 218 

Difference 38 Half sum do. 

As the sum of the sides, AB, AC, 218 

Is to their difference, 38 1.57978 

So is the tangent of half the sum of the { in °4QSS 



Sum of the angles B and C 131 48 

65 54 
- 2.33846 



angles B and C, 65° 54 



: 



11.92916 
To tang, of half their difference, 21° 17' - - 9.59070 
Half sum of the angles B and C - - 65° 54' 
Add and subtract half their difference - 21 17 



Angle C 87 11 



Angle B 44 37 



PLANE TRIGONOMETRY. 57 

To find the side BC. 

As sine of B, 44° 37' - - - 9.84656 
[s to sine of A, 48 12 - - -9.87243 
So is AC, 90 - - - 1.95424 



11.82667 



To BC, 95.52 1.98011 

By Gunter's Scale. 

Extend the compasses from 218, the sum of the sides, 
to 38, their difference, on the line of numbers, and apply 
this extent to the line of tangents from 45° to the left 
hand ; then keeping the left leg of the compasses fixed, 
move the other leg to 65° 54' the half sum of the angles ; 
that distance will reach from 45° on the same line, to 
21° 17', the half difference of the required angles. 
Whence the angles are obtained as before. 

To extend the second proportion, proceed as directed 
in Case 1st. 

2. In a triangle ABC, are given AB=109, BC=76, 
and the contained angle B=101° 30', to find the other 
angles and side. 

( Ans. The angle A=30°57', C=47° 33', and the 
{ side AC= 144.8. 

3. Given, in a right-angled triangle, the base AB=890 
and the perpendicular BC=787, to find the angles and 
hypothenuse. 

Ans. The angle A=41° 29', C=48° 3V, and 
the hypothenuse AC=1188. 
H 



{ 



58 PLANE TRIGONOMETRY. 

CASE 4. 

Given the three sides, to find the angles. 

1 RULE 1. 

Consider the longest side of the triangle as the base, 
and on it let fall a perpendicular from the opposite 
angle. This perpendicular will divide the base into 
two parts, called segments, and the whole triangle into 
two right-angled triangles. Then, 

As the base, or sum of the segments, 

Is to the sum of the other two sides ; 

So is the difference of those sides, 

To the difference of the segments of the base.* 



Fig. 48. * Demonstration. Let ABC, Fig. 48, be a 

triangle, and CD be perpendicular upon AB. 
About C as a centre, -with the less side BC for 
a radius, describe a circle, meeting AC pro- 
duced, in G and E, and AB in F. Then it is 
evident that AE is equal to the sum of the 
sides AC, BC, and that AG is equal to their 
difference; also because CD bisects FB (3.3,) 
it is plain that AF is the difference of the seg- 
ments of the base ; but AxBAF = AEx AG (36.3. cor. ;) therefore AB : 
AE : : AG : AF )16.6 ;) that is, the base, is to the sum of the sides, as 
the difference of the sides, is to the difference of the segments of the base. 
Cor. If AF be considered the base of the triangle AFC, then will CD 
be a perpendicular on the base produced ; AE will be equal to the sum of 
the sides AC, FC, and AG will be equal to their difference ; also AB will 
be equal to the sum of the . segments AD, FD. But by the preceding 
demonstration, and (16.5,) AF : AE : : AG : AB ; hence, when the per- 
pendicular falls without the triangle, the base is to the sum of the sides, 
as the difference of the sides is to the sum of the segments of the base. 

A rule might, therefore, be given, making either side of a triangle the 
base ; and such a rule would be rather more convenient, in some cases, 
than the one above : but then, on account of the perpendicular, sometimes 
falling within and sometimes without the triangle, it would require two 
cases, and consequently would be less simple. 




PLANE TRIGONOMETRY. 59 

To half the base, add half the difference of the seg- 
ments, and the sum will be the greater segment ; also 
from half the base, subtract half the difference of the 
segments, and the remainder will be the less segment. 

Then, in each of the two right-angled triangles, there 
will be known two sides, and an angle opposite to one 
of them ; consequently the other angles may be found 
by Case 2. 

1. In the triangle ABC, are given AB=426, AC = 
365, and BC = 230; required the angles. 

By Construction, Fig. 49. 

Draw AB=426 ; with AC = 365 in 
the dividers, and one foot in A, de- 
scribe an arc, and with BC=230, and 
one foot in B describe another arc, 
cutting the former in C ; join AC, BC, 
and ABC will be the triangle required. The angles 
measured by a scale of chords, will be A =32° 39', 
B = 58° 56', and C = 88° 25'. 

By Calculation. 

AC ------- 365 

BC 230 

Sum 595 

Difference ----- 135 




60 PLANE TRIGONOMETRY. 

As the base AB 426 2.62941 

Is to the sum of the sides AC, BC - 595 2.77452 
So is the diff. of the sides AC, BC - 135 2.13033 

4.90485 
To the diff. of the segments AD, DB 188.6 2.27544 

Half diff. of the segments - - - 94.3 
Half base 213. 

Segment AD 307.3 

Segment BD 118.7 

As AC 365 2.56229 

Is to AD 307.3 2.48756 

So is sine of ADC - - 90° 10.00000 

12.48756 

TosineofACD - - - - 57° 21' 9.92527 

90 00 

Angle A 32 39 

AsBC 230 2.36173 

IstoBD 118.7 2.07445 

So is sine of BDC - - - - 90° 10.00000 

12.07445 

To sine of BCD 31° 4' 9.71272 

90 

Angle B 58 56 

From 180° subtract the sum of the angles A, and B, 
91° 35', and the remainder 88° 25' is the angle C. 



PLANE TRIGONOMETRY. 61 

By Gunter's Scale. 

Extend the compasses from 426 to 595 on the line of 
numbers , that extent will reach on the same line from 
135 to 188.6 the difference of the segments of the base. 
Whence the segments of the base are found as before. 
To extend the other proportions, proceed as directed in 
Case 2. 

2. In a triangle ABC, there are given AB=64, AC— 
47, and BC=34 j required the angles. Ans. Angle A 
=31 6 9', B=45° 38', and C=103° 13'. 

3. In a triangle ABC, are given AC=88, AB=108, 
and BC=54, to find the angles. Ans. Angle A=29° 
49', B=54° 7, and C=96° 4'. 

RULE 2. 

Add together the arithmetical complements of the lo- 
garithms of the two sides containing the required angle, 
the logarithm of the half sum of the three sides, and the 
logarithm of the difference between the half sum and 
the side opposite the required angle. Then half the 
sum of these four logarithms will be the logarithmic 
cosine of half the required angle.* 



* Demonstration. Let ABC, be a triangle of which the side AB, is 
greater than AC: make AD=AC, join DC, bisect it in E, and join AE; 
draw EH parallel and equal to CB ; join HB and produce it to meet AE 
produced in G. 

Now in the triangles AED, AEC, 
all the sides of the one are equal 
to the sides of the other, each to 
each ; therefore (8.1) the angle EAD 
=EAC, and AED= AEC ; consequent- 
ly AED is a right angle. 




62 



PLANE TRIGONOMETRY. 
EXAMPLES. 



1. In the triangle ABC, are given AB=426, AC=365 
and BC=230; required the angle A. 



By Calculation, 




BC 230 
AC 365 
AB 426 


Ar. Co. 

Ar. Co. 


7.43771 
7.37059 


2)1021 
Half sum 510.5 


log. 
log. 


2.70800 


Difference 280.5 


2.44793 






2)19.96423 


Cos. iA 16° 20 
2 


i 


9.98211 


Angle A 32 40 





Because EH is equal and parallel to BC, BH is also equal and parallel to 
EC (33.1 ;) now in the triangles EDF and HBF, the angle EFD—BFH, the 
angle FED=FHB (29.1) and ED=EC=BH; therefore (26.1) EF=FH,and 
FD=FB. Again, the angle HGE=DEA=a right angle; if therefore 
■with the centre F, and radius FE=FH, a circle be described, it will pasi 
through the point G (31.3.) 

Now2AF=2AD + 2DF=AD-fAD + DB=AD-fAB=AC+AB; there- 
fore AF=£AC+£AB ; also FK=|IK=pH=pC ; hence, by adding equals 
to equals, AF+FK=£AC+iAB+pC, or AK=£(AC+AB+BC;) again, 
AI= AK— IK=^(AC-f- AB+ BC)— BC. 

But (Dem. to rule, case 1st.) AD : AE : : sin. AED : sin. ADE : : rad. : cos. 
EAD (cos. ABAC.) Also, AB : AG : : sin. AGB : sin. ABG : : rad.: cos. 
BAG (cos. £BAC.) 

Hence (c. 6) AB x AD : : AG x AE : : rad. 2 : (cos. £BAC) 2 . But AB x 
AD=ABxAC,and (cor.36.3) AGx AE=AKx AI=4(AC+AB+BC)x 
[$(AC+AB+BC)— BC;] therefore ABxAC: i(AC+AB-(-BC)x[KAC-- 
AB+BC)— BC] : : rad. 2 : (cos. £BAC) 2 . 

Now it is evident, that in working this proportion by logarithms 



PLANE TRIGONOMETRY. 



63 



If the other angles are required, they may be found 
by Case 1. 

2. In a triangle ABC, are given AB = 64, AC =4 7, 
and BC=34, to find the angle B. Ans. Angle B= 

45° 38'. 

3. In a triangle ABC, are given AC= 88, AB=108, 
and BC = 54, to find the angle C. Ans. C = 96° 4'. 

The preceding rules solve all the cases of plane trian- 
gles, both right-angled and oblique. There are, how- 
ever, other rules, suited to right-angled triangles, which 
are sometimes more convenient than the general ones. 
Previous to giving these rules, it will be necessary to 
make the following 



Fig. 50. 



Remarks on right-angled triangles. 

1. ABC, Fig. 50, being a right-angled 
triangle, make one leg AB radius, that is, 
with the centre A, and distance AB, de- 
scribe an arc BF. Then it is evident that 
the other leg BC represents the tangent of 
the arc BF, or of the angle A, and the hypothenuse 
AC the secant of it. 




2. In like manner, if the leg BC, Fig. 51, 
be made radius • then the other leg AB will 
represent the tangent of the arc BG, or 
angle C, and the hypothenuse AC the secant 
of it. aZ 



Fig. 51. 




Tang. C 



and taking the arithmetical complements of the logarithms of the first 
term, viz. of the two sides, including the required angle, if we omit the 
logarithm of the square of radius, which is 20, it is just equivalent to re- 
jecting 20 from the sum of the logarithms, which would otherwise have 
to be done. 



64 PLANE TRIGONOMETRY. 

Fig. 52. 3. g u t if the hypothenuse be made 

radius, then each leg will represent the 
\ sine of its opposite angle ; namely, the 
\ leg AB, Fig. 52, the sine of the arc AE 
— !d or angle C, and the leg BC the sine of 
j£ the arc CD, or angle A. 

TJie angles and one side of a right-angled triangle heing 
given, to find the other sides. 

RULE. 

Call any one of the sides radius, and write upon it 
the word radius ; observe whether the other sides be- 
come sines, tangents, or secants, and write these words 
on them accordingly. Call the word written upon each 
side the name of that side. Then, 

As the name of the side given, 

Is to the name of the side required ; 

So is the side given, 

To the side required.* 

Two sides of a right-angled triangle being given, to find 
the angles and other side. 

RULE. 

Call either of the given sides radius, and write on 
them as before. Then, 

Fig,. 53. * Demonstration. Let ABC, Fig. 53, be a right- 

y\ angled triangle ; then it is evident that BC is the tan- 
c y-'* \ ] gent, and AC the secant of the angle A, to the radius 
\j AB. Let AD represent the radius of the tables, and 
! D draw DE perpendicular to AD, meeting AC produced 
in E ; then DE is the tangent, and AE the secant of 
the angle A, to the radius AD. But because of the similar triangles 
ADE, ABC, AD : DE : : AB : BC ; that is, the tabular radius : tabular 
tangent : : AB : BC. Also AD : AE : : AB : AC ; that is, the tabular 
radius : tabular secant : : AB : AC. These proportions correspond with 
the rule. When either of the other sides is made radius, the demonstra- 
tion will be similar. 






PLANE TRIGONOMETRY. 65 

As the side made radius, 
Is to the other given side ; 
So is radius, 
To the name of that other side.* 

After finding the angle, the other side is found as in 
the preceding rule. 

EXAMPLES. 

1. In a right-angled triangle ABC, are given the base 
AB=208, and the angle A=35° 16', to find the hypo- 
thenuse AG and perpendicular BC. 



By Calculation, 

The hypothenuse AC being radius. 
As the sine of C, 54° 44' - - - 9.91194 
Is to radius ------ 10.00000 

So is AB 208 2.31806 

12.31806 

To AC 254.8 ------ 2.40612 

As the sine of C 54° 44' - - - 9.91194 
Is to the sine of A, 35 16 - - - 9.76146 
So is AB 208 2.31806 

12.07952 

To BC, 147.1 2.16758 



* This is the converse of the preceding rule. 
6* I 



66 PLANE TRIGONOMETRY. 

The base AB being radius. 

As radius 10.00000 

Is to the secant of A, 35° 16' - - 10.08806 
So is AB 208 2.31806 

12.40612 

To AC 254.8 2.40612 

As radius 10.00000 

Is to tangent of A, 35° 16' - - 9.84952 
So is AB, 208 2.31806 

12.16758 

To BC 147.1 2.16758 

The perpendicular BC being radius. 
As tangent of C 54° 44' - - - -10.15048 
Is to secant of C, 54 44 - - - -10.23854 
SoisAB, 208 • 2.31806 

12.55660 

To AC 254.8 - 2.40612 

As tangent ofC, 54° 44'- - - - 10.15048 

Is to radius, 10.00000 

SoisAB 208 2.31806 

12.31806 

To BC, 147.1 2.16758 

2. In a right-angled triangle ABC, there are given the 
hypothenuse AC =272, and the base AB=232 ; required 
the angles A and C, and the perpendicular BC. 



PLANE TRIGONOMETRY. 67 

By Calculation, 

The hypothenuse AC being radius. 

As AC, 272 2.43457 

Is to AB, 232 2.36549 

So is radius 10.00000 



12.36549 



To sine of C, 58° 32* - - - - 9.93092 

As radius 10.00000 

Is to sine of A, 31° 28' - - - - 9.71767 
So is AC, 272 2.43457 

12.15224 

ToBC, 142 - 2.15224 

The base AB being radius. 

AsAB,232 2.36549 

Is to AC, 272 2.43457 

So is radius 10.00000 

12.43457 

To secant of A, 31° 28* - - - - 10.06908 

As radius 10.00000 

Is to tangent of A, 31° 28' - - - 9.78675 
So is AB, 232 2.36549 

12.15224 

ToBC, 142 2.15224 



68 PLANE TRIGONOMETRY. 

3. In a right-angled triangle, are given the hypothe- 
nuse AC==36.57, and the angle A=27° 46', to find the 
base AB, and perpendicular BC. 

Ans. Base AB=32.36, and perpendicular BC=17.04. 

4. In a right-angled triangle, there are given, the per- 
pendicular=193.6, and the angle opposite the base 47° 
51'; required the hypothenuse and base. 

Ans. Hypothenuse=288.5, and base=213.9. 

5. Required the angles and hypothenuse of a right- 
angled triangle, the base of which is 46.72, and perpen- 
dicular 57.9. 

- ( Angle opposite the base 38° 54', angle opposite 
( the perpendicular 51° 6', and hypothenuse 74.4. 

When two sides of a right-angled triangle are given, 
the other side may be found by the following rules, with- 
out first finding the angles. 

1. When the hypothenuse and one leg are given, to find 
the other leg. 

RULE. 

Subtract the square of the given leg from the square 
of the hypothenuse ; the square root of the remainder 
will be the leg required.* Or by logarithms thus, 

To the logarithm of the sum of the hypothenuse and 
given side, add the logarithm of their difference ; half 
this sum will be the logarithm of the leg required. 



* Demonstration. The square of the hypothenuse of a right-angled tri- 
angle is equal to the Bum of the squares of the sides (47.1.) Therefore the 
truth of the first part of each of the rules is evident 



PLANE TRIGONOMETRY. 69 

2. When the two legs are given to find iJie hypothenuse. 

RULE. 

Add together the squares of the two given legs ; the 
square root of the sum will be the hypothenuse.* Or 
by logarithms thus, 

From twice the logarithm of the perpendicular, sub- 
tract the logarithm of the base, and add the correspond- 
ing natural number to the base ; then, half the sum of 
the logarithms of this sum, and of the base, will be the 
logarithm of the hypothenuse. 

EXAMPLES. 

1. The hypothenuse of a right-angled triangle is 272, 
and the base 232 ; required the perpendicular. 

Calculation by logarithms, 

Hypothenuse - - 272 
Base - - - - 232 

Sum .... 504 log. 2.70243 
Difference - - - 40 1.60206 



2)4.30449 



Perpendicular - - 142 2.15224 

* Put A=the hypothenuse, 6=the base, and p=the perpendicular, 

then (47.1) f=h 2 — o*=(5.2 cor.) h+bxh^ or p^y/h+bxh^; 
whence, from the nature of logarithms, the latter part of the first rule 
is evident 



Also (47.1) h 2 =V+p>=bXb+PL or k=^/ (bxb+£ ) 
b \ b ' 

which, solved by logarithms, will correspond with the latter part of the 
second rule. 



70 APPLICATION OF 

2. Given the base 186, and the perpendicular 152, 
to find the hypothenuse. 

Calculation by Logarithms. 



Perpendicular 


152 log. 

186 

124.2 

310.2 

240.2 


2.18184 

2 


Base - - - 


4.36368 

2.26951 2.26951 




2.09417 

log. 2.49164 


Hypothenuse 


2)4.76115 
log. 2.38057 



3. The hypothenuse being given equal 403, and one 
leg 321 ; required the other leg. Arts. 243.7. 

4. "What is the hypothenuse of a right-angled triangle, 
the base of which is 31.04 and perpendicular 27.2? 

Ans. 41.27. 

The following examples, in which trigonometry is 
applied to the mensuration of inaccessible distances and 
heights, will serve to render the student expert in solv- 
ing the different cases, and also to elucidate its use. 

Fig. 54. THE APPLICATION OF PLANE TRIGONO- 

METRY TO THE MENSURATION OF DIS- 
TANCES AND HEIGHTS. 




EXAMPLE 1, Fig. 54. 

Being on one side of a river and want- 
ing to know the distance to a house on the other side, 



PLANE TRIGONOMETRY. 71 

I measured 500 yards along the side of the river in a 
right line AB, and found the two angles* between this 
line and the object to be CAB = 74° 14' and CBA=49° 
23'. Required the distance between each station and 
the object. 

Calculation. 

The sum of the angles CAB and CBA is 123° 37', 
which subtracted from 180° leaves the angle ACB = 
56° 23'. Then by Case 1 ; 

s. ACB : s. CBA : : AB : AC 

56° 23' 49° 23' 500 455.8 

and 

s. ACB : s. CAB : : BA : BC 

5G°23' 74° 14' 500 577.8 



EXAMPLE 2, Fig. 55. 

Suppose I want to know the dis- Fi s- 55 - 

tance between two places, A and B, »«*=««*. -^S" 

accessible at both ends of the line AB, A^gg^y 
and that I measured AC = 735 yards, 
and BC= 840 ; also the angle ACB = 
55° 40'. What is the distance be- 
tween A and B ? 



v 



Calculation. 

The angle ACB =55° 40', being subtracted from 
180°, leaves 124° 20'; the half of which is 62° 10'. 
Then by Case 3, 

* The angles may be taken with a common surveyor's compass ; or 
more accurately with an instrument called a theodolite. 



72 



APPLICATION OF 



BC + AC : BC— AC : : tangent ~~ 
1575 105 62° 10 

CAB+CBA 



CAB+CBA . CAB— CBA 

2 ' tangent 



To and from 



2 

7° 12' 

CAB-CBA 

= 62° 10' add and sub. 2 



12', and we shall have CAB = 69° 22', and CBA = 54° 58'. Then, 



s. ABC 

54° 58' 



s. ACB 

55° 40' 



: AC 
735 



AB 

741.2 



Fig. 56. 




EXAMPLE 3, Fig. 56. 

Wanting to know the distance 
between two inaccessible objects 
A and B, I measured a base line 
CD = 300 yards: at C the angle 
BCD was 58° 20' and ACD 95° 
20'; at D the angle CDA was 
53° 30' and CDB 98° 45'. Re- 
quired the distance AB. 

Calculation. 

1. In the triangle ACD, are given the angles ACD = 
95° 20', ADC = 53° 30', and the side CD =300, to find 

AC =465.98. 

2. In the triangle BCD, are given the angle BCD= 
58° 20', BDC = 98° 45', and side CD=300, to find BC 
= 761.47. 

3. In the triangle ACB we have now given the angle 
ACB = ACD— BCD =37°, the side AC = 465.98 and 
BC = 761.47, to find AB = 479.8 yards, the distance 
required. 



Fig. 57. 




EXAMPLE 4, Fig. 57. 

Being on one side of a river 
and observing three objects, A, 
B and C stand on the other 
side, whose distances apart I 
knew to be, AB = 3 miles, AC 



PLANE TRIGONOMETRY. 73 

= 2, and BC = 1.S, I took a station D, in a straight line 
with the objects A and C, being nearer the former, and 
found the angle ADB =17° 47'. Required my distance 
from each of the objects. 

Construction. 

With the three given distances, describe the triangle 
ABC ; from B, draw BE parallel to CA, and draw BD 
making the angle EBD=17° 47' (the given angle ADB) 
and meeting CA produced, in D : then AD, CD and BD 
will be the distances required.* 

Calculation. 

1. In the triangle ABC we have all the sides given, 
to find the angle C=104° 8'. 

2. Subtract the sum of the angles D and C from 
180°, the remainder 58° 5' will be the angle DBC ; then 
in the triangle BCD we know all the angles and the 
side BC to find DC=5.002 and BD=5.715; therefore 
DA=DC— AC = 3.002. 

EXAMPLE 5, Fig. 58. 

From a station at D, I perceived 
three objects, A, B and C, whose 
distances from each other I knew 
to be as follows : AB= 12 miles, BC 
= 7.2 miles, and AC =8 miles; at 
D, I took the angle CDB=25° and 
ADC = 19°. Hence it is required 
to find my distance from each of 
the objects. 

* Demonstration. By construction, the distances AB, BC and AC are 
equal to the given distances; also the angle (29.1) BDC = the angle DBE 
=the given angle. 

7 K 




74 APPLICATION OF 

Construction. 

With the given distances describe the triangle ABC ; 
at B, make the angle EBA=19°=the given angle ADC, 
and at A, make the angle EAB=25°=the given angle 
BDC ; draw AE, and BE meeting in E, and (by prob. 10,) 
describe a circle that shall pass through the points A, 
E and B : join CE and produce it to meet the circle in 
D, and join AD, BD, then will AD, CD, and BD be the 
distances required.* 

Calculation. 

1. In the triangle ABC, all the sides are given, to find 
the angle BAC=35° 35'. 

2. In the triangle AEB, are given all the angles, viz. 
EAB=25°, EBA=19°,and AEB=136°, and the side 
AB=12, to find AE=5.624. 



* Demonstration. The angle ADC standing on the same arc with the 
angle ABE is equal to it (21.3.) For the same reason the angle BDC 
is equal to the angle BAE; but by construction the angles ABE and BAE 
are equal to the given angles ; therefore the angles ADC and BDC are equal 
to the given angles. 

Note. — When the given angles ADC, BDC are respectively equal to the 
angles ABC, BAC, the point E will fall on the point C, the circle will pass 
through the points A, C, and B, and the point D may be any where in the 
arc ADB ; consequently, in this case, the situation of the point D, or its 
distance from each of the objects A, B, C, cannot be determined from the 
data given. 

It may not be improper also to observe, that even when the angle ADB, 
which is the sum of the given angles, is equal to the sum of the angles ABC, 
BAC, o\ which is the same thing, is the supplement of the angle ACB, the 
circle passes through the points A, C, B ; but then the angles ADC, BDC, 
unless they have been erroneously taken, will be respectively equal to the 
angles ABC, BAC. 



PLANE TRIGONOMETRY. 75 

3. In the triangle CAE we have given the side AC 
-8, AE=5.624, and the angle CAE=BAC— EAB = 
10° 35', to find the angle ACE=22° 41'. 

4. In the triangle DAC, all the angles are given, 
viz. ADC=19°, ACD=22° 41' and CAD=180°— the 
sum of the angles ADC and ACD=138° 19', and the 
side AC=8, to find AD=9.47 miles, and CD=16.34. 

In the triangle ABD, we have the angle ADB= ADC 
+BDC=44°, the angle BAD=CAD— BAC=102°44', 
and the side AB=12, to find BD=16.85 miles. 

EXAMPLE 6, Fig. 59. 
A person having a triangular field, 
the sides of which measure AB=50 
perches, AC =46 perches, and BC = 
40 perches, wishes to have a well 
dug in it, that shall be equally dis- 
tant from the corners A, B and C. 
What must be its distance from each 
corner, and by what angle from the 
corner A, may its place be found ? 

Construction. 
With the given sides construct the triangle ABC, 
and (by Prob. 10.) describe a circle that shall pass 
through the points A, B, and C j then the centre E of 
this circle is the required place of the well* 

Calculation. 

1. In the triangle ABC, all the sides are given, to 
find the angle ABC=60° 16'. 

2. Join CE and produce it to meet the circumference 
in D ; also join AE and AD ; then the angles ADC, ABC 

* The demonstration of this is plain (1.3 cor.) 




76 



APPLICATION OF 



being angles in the same segment, are equal ; also the 
angle DAC being an angle in a semicircle, is a right-an- 
gle : therefore in the right-angled triangle DAC, we have 
the angle ADC = ABC = 60° 16', and the side AC, to find 
CD= 52.98 perches. The half of CD is= 26.49 perches 
= CE=the distance of the well from each corner. 

3. The angle ACD = 90°— ADC=29° 44; but be- 
cause AEC is an isosceles triangle, the angle CAE= 
ACE =29° 44' the angle required. 



example 7, Fig. 61. 



Fig. 61. 




Wishing to know the height of 
a steeple situated on a horizontal 
plane, I measured 100 feet in a 
right line from its base, and then 
took the angle of elevation* of the 
top, which I found to be 47° 30', 
the centre of the quadrant being 5 
feet above the ground : required 
the height of the steeple. 




* Angles of elevation, or of depression, 
are usually taken with an instrument called 
a quadrant, the arc of which is divided into 
90 equal parts or degrees, and those, when 
the instrument is sufficiently large, may be 
subdivided into halves, quarters, &c. From 
the centre a plummet is suspended by a fine 
silk thread. Fig. 60 is a representation of 
this instrument. 

To take an angle of elevation, hold the quadrant in a vertical position, 
and the degrees being numbered from B towards C, with the eye at C, 
look along the side CA, moving the quadrant till the top of the object is 
seen in a range with this side ; then the angle BAD made by the plummet 
with the side BA, will be the angle of elevation required. 

Angles of depression are taken in the same manner, except that then 
the eye is applied to the centre of the quadrant. 

Note. — In finding the height of an object, it is best to take such a posi- 
tion that the observed angle of altitude may be about 45° ; for when the 
observed angle is 45°, a small error committed in taking it, makes the 
least error in the computed height of the object. 



PLANE TRIGONOMETRY. 



77 




Calculation. 
In the right-angled triangle DEC, we have the angle 
CDE=47° 30', and the base DE = AB = 100 feet, to 
find CE = 109.13 feet; to CE add EB = DA = 5 feet, 
the height of the quadrant, and it will give BC = 
114.13 feet, the required height of the steeple. 

example 8, Fig. 62. 
Wishing to know the height of 
a tree situated in a bog, at a sta- 
tion D, which appeared to be on 
a level with the bottom of the 
tree, I took the angle of eleva- 
tion BDC = 51-° 30'; I then measured DA =75 feet in 
a direct line from the tree, and at A, took the angle of 
elevation BAC=26° 30'. Eequired the height of the 
tree. 

Calculation. 

1. Because the exterior angle of a triangle is equal 
to the sum of the two interior and opposite ones, the 
angle BDC = DAC + ACD; therefore ACD = BDC— 
DAC = 25° : now in the triangle ADC we have DAC= 
26° 30', ACD = 25°, and AD=75, to find DC = 79.18. 

2. In the right-angled triangle DBC are given DC = 
79.18, and the angle BDC=51° 30' to find BC=61.97 
feet, the required height of the tree. 

example 9, Fig. 63. 
Wanting to know the 
height of a tower EC, 
which stood upon a hill, 
at A, I took the angle of 
elevation CAB=44°; I 
then measured AD 134 
yards, on level ground, in 
a straight line towards the 
7* 




78 



APPLICATION OF 



tower; at D the angle CDB was 67° 50' and EDB 51°. 
Required the height of the tower and also of the hill. 

Calculation. 

1. In the triangle ADC we have the angle DAC = 
44°, the angle ACD=BDC— DAC=23° 50', and the 
side AD, to find DC=230.4. 

2. In the triangle DEC all the angles are given, viz. 
CDE=BDC— BDE = 16° 50', DCE=90°— BDC=22° 
10', DEC=180°=the sum of the angles CDE and DCE 
=141°, and CD=230.4, to find CE=106 yards, the 
height of the tower. 

3. In the right-angled triangle DBC, we have the 
angle BDC = 67° 50', and the side DC=230.4, to find 
BC== 213.4; then BE=BC—CE=213.4— 106=107.4 
yards, the height of the hill. 



Fig. 64. 




EXAMPLE 10, Fig. 64. 

An obelisk AD standing 
on the top of a declivity, I 
measured from its bottom 
a distance AB=40 feet, 
and then took the angle 
ABD=41°; going on in 
the same direction 60 feet 
farther to C, I took the an- 
gle ACD=23° 45': what 
was the height of the obelisk ? 

Calculation. 

1. In the triangle BCD, we have given the angle 
BCD=23° 45', the angle BDC= ABD— BCD=17° 15', 
and side BC=60, to find BD = 81.49. 

2. In the triangle ABD are given the side AB=40, 
BD=81.49, and the angle ABD=41°, to find AD= 
57.64 feet, the height of the obelisk. 



PLANE TRIGONOMETRY. 



79 



Fig. 65. 




EXAMPLE 11, Fig. 65 

Wanting to know the height 
of an object on the other side of 
a river, but which appeared to 
be on a level with the place 
where I stood, close by the side 
of the river; and not having 
room to go backward on the same plane, on account of 
the immediate rise of the bank, I placed a mark where 
I stood, and measured in a direct line from the object, 
up the hill, whose ascent was so regular that I might 
account it a right line, to the distance of 132 yards, 
where I perceived that I was above the level of the top 
of the object ; I there took the angle of depression of 
the mark by the river's side equal 42°, of the bottom 
of the object equal 27°, and of its top equal 19° : re- 
quired the height of the object. 

Calculation. 

1. In the triangle ACD, are given the angle CAD= 
EDA=27°, ACD=180°— CDE (FCD)=138°, and the 
side CD=132, to find AD=194.55 yards. 

2. In the triangle ABD, we have given ADB= ADE — 
BDE = 8°,ABD=BED+BDE=109°andAD=194.55, 

to find AB= 28.64 yards, the required height of the 
object. 

EXAMPLE 12, Fig. 66. 
A May-pole whose height was 100 feet stand- 
ing on a horizontal plane, was broken by a 
blast of wind, and the extremity of the top 
part struck the ground at the distance of 34 
feet from the bottom of the pole : required the 
length of each part. 



Fig. 66. 




80 APPLICATION OF 

Construction. 

Draw AB=34, and perpendicular to it, make BC= 
100 ; join AC and bisect it in D, and draw DE perpendi- 
cular to AC, meeting BC in E ; then AE=CE=the part 
broken off.* 

Calculation. 

1. In the right-angled triangle ABC, we have AB=34 
and BC=100, to find the angle C=18° 47'. 

2. In the right-angled triangle ABE, we have AEB= 
ACE+CAE=2ACE=37° 34', and AB=34, to find AE 
=55.77 feet, one of the parts; and 100-55.77=44.23 
feet the other part. 

PRACTICAL QUESTIONS. 

1. At 85 feet distance from the bottom of a tower, the 
angle of its elevation was found to be 52° 30': required 
the altitude of the tower. Ans. 110.8 feet. 

2. To find the distance of an inaccessible object, I 
measured a line of 73 yards, and at each end of it took 



* Demonstration. In the triangles AED, DEC, the angle ADE=CDE, 
the side AD=CD, and DE is common to the two triangles, therefore (4.1) 
AE=CE. 

JSote. — This question may be neatly solved in the following man- 
ner without finding either of the angles. Thus, draw DF perpendi- 
cular to BC, then (31.3 and cor. 8.6) FC : DC : : DC : CE ; cons©- 

DC2 , ™, AC 2 AF+BC» , m , ^ 

qnently CE=pg ; but DC 2 =~ 1 -= J , and FC=£BC ; there- 

AB 2 +BC 2 34 2 +100 J 1156+10000 11156____ Q .. 

fore CE=-2BC" = "200 = 200 = ~~ 200~ _55 - 79 ' th ° 

same as before nearly. 



PLANE TRIGONOMETRY. 81 

the angle of position of the object and the other end, and 
found the one to be 90°, and the other 61° 45': required 
the distance of the object from each station. Ans. 135.9 
yards from one, and 154.2 from the other. 

3. Wishing to know the distance between two trees 
C and D, standing in a bog, I measured a base line AB= 
339 feet ; at A the angle BAD was 100° and BAC 36° 30'; 
at B the angle ABC was 121° and ABD49 : required the 
distance between the trees. Ans. 697i feet. 

4. Observing three steeples, A, B and C, in a town at a 
distance, whose distances asunder are known to be as 
follows, viz. AB=213, AC=404, and BC=262 yards, I 
took their angles of position from the place D where I 
stood, which was nearest the steeple B, and found the 
angle ADB=13° 30'; and the angle BDC=29° 50'. Re- 
quired my distance from each of the three steeples. Ans. 
AD=571 yards, BD=389 yards, and CD=514 yards. 

5. A May-pole, whose top was broken off by a blast 
of wind, struck the ground at 15 feet distance from the 
foot of the pole : what was the height of the whole May- 
pole, supposing the length of the broken piece to be 39 
feet ? Ans. 75 feet. 

6. At a certain place the angle of elevation of an in- 
accessible tower was 26° 30 f ; but measuring 75 feet in 
a direct line towards it, the angle was then found to be 
51° 30': required the height of the tower and its distance 
from the last station. Ans. Height 62 feet, distance 
49. 

7. From the top of a tower by the sea side, of 143 feet 
high, I observed that the angle of depression of a ship's 

L 



82 APPLICATION, &C. 

bottom, then at anchor, was 35° ; what was its distance 
from the bottom of the wall 1 Am. 204.2 feet. 

8. There are two columns left standing upright in the 
ruins of Persepolis ; the one is 64 feet above the plane, 
and the other 50 ; in a right line between these stands 
an ancient statue, the head of which is 97 feet from the 
summit of the higher, and 86 from that of the lower 
column; and the distance between the lower column 
and the centre of the statue's base is 76 feet : required 
the distance between the tops of the columns. 

Ans. 157 feet. 



SURVEYING. 



CHAPTER I. 

ON THE DIMENSIONS OF A SURVEY. 

1. Surveying is the art of measuring, laying out and 
dividing land. 

2. A Four-Pole Chain is an instrument used for mea- 
suring the boundaries of a survey. It is, as its name im- 
ports, 4 poles or 66 feet in length, and is divided into 100 
equal parts or links. The length of a link is therefore 
7.92 inches. 

Note. — A Four-pole Chain is frequently called simply 
a chain. 

3. A Two-pole Chain is 2 poles or 33 feet in length, 
and is usually divided into 50 equal parts or links. 
When it is thus divided, the links are of the same length 
as in a four-pole chain ; and the measures taken with 
it are reduced to four-pole chains previous to using them 
in calculation. 

Sometimes the two-pole chain is divided into 40 links ; 
in which case, each two links is the one-tenth of a perch. 
Measures taken with a two-pole chain, thus divided, are 
usually expressed in perches and tenths. 



84 DIMENSIONS OF A SURVEY. [dlAP. I. 

4. The Distance of a line in surveying, is its length, 
estimated in a horizontal direction. It is generally ex- 
pressed either in chains and links, or in perches and 
tenths. 

5. A Meridian or Meridian Line is any line that runs 
due north or south. 

Note. — All the meridians passing through any survey 
of moderate extent may be considered as straight lines, 
parallel to one another.* 

6. The Bearing or Course of a line, is the angle 
which it makes, with a meridian passing through one 
end ; and it is reckoned from the North or South Points 
of the horizon towards the East or West Points. 

Fig. 77. ^ Thus, supposing the line NS, Fig. 
77, to be a meridian, and the angle 
SAB to be 50° ; then the bearing of 
AB from the point A, is 50° to the 
east of south ; which is usually ex- 
pressed thus : S. 50° E, and read, 
south, fifty degrees east. 

7. The Reverse Bearing of a line is 
ie bearing 
of the line. 



the bearing taken from the other end 



Note. — The bearing and the reverse bearing of a line, 
are angles of the same magnitude,f but lying between 

* The meridians are, in reality, curve lines which meet in the north 
and south poles of the earth. No two of them are therefore exactly 
parallel ; but in usual surveys their deviation from parallelism is so very 
small, that there is no sensible error in considering them so. 

f As the meridians are not exactly parallel, this is not strictly true, except 
in a few cases ; but the difference is too small to be observed in practice. In 



CHAP. I.J DIMENSIONS OF A SURVEY. 85 

directly opposite points. Thus, if the bearing of AB, 
from the end A, is S. 50° E., the bearing of the same line 
from the end B, is N. 50° W. 

8. A Circumferentor or Surveyors Compass, is an in- 
strument used to take the bearings of lines. 

The circumference of its face is divided into degrees, 
and in some of the larger ones into half degrees, in such 
manner that two opposite points may be exactly in the 
direction of the sights with which the instrument is fur- 
nished. These points are the north and south points of 
the instrument. Midway between them, on the circum- 
ference, are the east and west points. The degrees are 
numbered from 0° to 90°, each way from the north and 
south points to the east and west ones. In the centre 
of the face is a pin, finely pointed, which supports a 
Magnetic Needle, moving freely within the instrument. 
The instrument, when used, is placed on a staff, having 
a pointed iron at the bottom, and a ball and socket at 
the top. 

The Chain and Compass are the instruments with 
which the dimensions of surveys in this country are 
generally taken. It is important to have them accurately 
made. In the selection of a compass, particular atten- 
tion should be directed to the settling of the needle. If, 
when the needle has been moved out of its natural posi- 
tion, it settles very soon, it is defective ; either its mag- 
netic virtue is weak, or it does not move with sufficient 
freedom on the pin. 

9. The Difference of Latitude, or the Northing or 



the latitude of Philadelphia the greatest difference between the bearing and 
reverse bearing of a line, a mile in length, is only 44". In higher latitudes 
the difference is greater. 

8 



86 DIMENSIONS OF A SURVEY. [CHAl\ I. 

Southing of a line, is the distance that one end is further 
north or south than the other end ; or it is the distance 
which is intercepted on a meridian passing through one 
end, between this end and a perpendicular to the meri- 
dian, from the other end. 

Thus, if NS, Fig. 77, be a meridian passing through 
the end A, of the line AB, and B6 be perpendicular to 
NS, then is Ah the difference of latitude or southing of 
AB. 

10. The Departure or the Easting or Westing of a line 
is the distance that one end is further east or west than 
the other end ; or it is the distance from one end, perpen- 
dicular to a meridian passing through the other end. 

Thus Bb, Fig. 77, is the departure or easting of the 
line AB. 

But if ns be a meridian, and AC perpendicular to it, 
and if the bearing of the line be taken from B to A, then 
is BC the difference of latitude or northing, and AC the 
departure or westing, of the line AB. 

Note. — It is evident from the definitions, that the Dis- 
tance, Difference of Latitude, and the Departure form the 
sides of a right-angled triangle ; in which, considering 
the departure as the base, the perpendicular is the differ- 
ence of latitude, the hypothenuse is the distance, and the 
angle at the perpendicular is the bearing. 

11. The Meridian Distance of any station, is its dis- 
tance from a meridian passing through the first station 
of the survey, or any other assumed point. 

12. The Traverse Table, is a table containing the dif- 



CHAP. I.] DIMENSIONS OF A SURVEY. 87 

ferences of latitude and the departures, computed to dif- 
ferent courses and distances. 

13. The Area or Content of a tract of land is the hori- 
zontal surface included within its boundaries, expressed 
in known measures, as Acres, Roods, and Perches. 

14. In going round a tract of land and returning to 
the place of beginning, it is evident that the whole 
northing which has been made, must be equal to the 
southing, and the easting to the westing ; or in other 
words, that the sum of all the northings must be equal 
to that of the southings, and the sum of the eastings, to 
that of the westings. 

This principle enables us to judge of the accuracy of 
a survey, when the bearings and distances of all the sides 
have been taken. If the sums of the computed north- 
ings and southings are equal, and also those of the east- 
ings and westings ; or, if, though not exactly equal, they 
are very nearly so, we may conclude that the survey has 
been correctly made ; as very small differences in these 
sums may be imputed to little, unavoidable errors in 
taking the bearings and measuring the distances. But 
when the sum of the northings diners considerably from 
that of the southings, or that of the eastings from that 
of the westings, we must infer that an error has been 
made, too great to be admitted. In this case a re-sur- 
vey should be taken. 

It is a rule with some of our best practical surveyors, 
that when the difference between the sums of the north- 
ings and southings, called the error in latitude, or that 
between the sums of the eastings and westings, called 
the error in departure, exceeds one link for every five 
chains in the sum of the distances, a re-survey ought to 
be made. 



88 DIMENSIONS OF A SURVEY. [cHAP. I. 

When the errors in latitude and departure fall within 
the limits just mentioned, they should be properly appor- 
tioned among the several latitudes* and departures ; we 
shall thus obtain what are called the corrected latitudes 
and departures. The method of doing this will be given 
in one of the following problems. 

PROBLEM I. 

To reduce two-pole chai?is and links to four-pole chains 
and links. 

RULE. 

1. If the number of chains is even, divide it by 2, and 
to the quotient annex the given number of links. 

2. If the number of chains is odd, divide by 2 as be- 
fore, for the chains ; and for the 1 that is off, add 50 to 
the given number of links. 

EXAMPLES. 

1. In 16 two-pole chains and 37 links, how many four- 
pole chains and links 1 Ans. 8 ch. 37 links, or 8.37 ch. 

2. How many four-pole chains and links are there in 
17 two-pole chains and 42 links 1 Ans. 8.92 ch. 

3. How many four-pole chains and links are there in 
22 two-pole chains and 7 links ? Ajis. 1 1 .07 ch. 



* In order to conciseness of expression, difference of latitude is frequently 
called simply, latitude. 



CHAP. I.] DIMENSIONS OF A SURVEY. 39 

PROBLEM II. 

To reduce two-pole chains and links to perches and 
hundredths of a perch, 

RULE. 

Multiply the links by 4, for the hundredths, and the 
chains by 2, for the perches. If the hundredths exceed 
100, set down the excess, and add 1 to the perches. 

Note. — This rule supposes the two-pole chain to be di- 
vided into 50 links. 

EXAMPLES. 

1. Reduce 17 two-pole chains and 21 links to perches 
and hundredths. Ans. 34.84 per. 

2. Reduce 15 two-pole chains and 38 links to perches 
and hundredths. Ans. 31.52 per. 

3. Reduce 57 two-pole chains and 49 links to perches 
and hundredths. Ans. 115.96 per. 

PROBLEM III. 

To reduce square four-pole chains to acres. 



Divide by 10, and the quotient will be the acres. If 
there is a decimal in the quotient, multiply it by 4, for 
the roods; and the decimal of these py 40, for the 
perches. 

8* M 



90 DIMENSIONS OF A SURVEY. [cHAP. I. 

EXAMPLES. 

1. Reduce 523.2791 square chains to acres. 
10)523.2791 



52.32791 
4 

1.31164 
40 



12.46560 Ans. 52 ac. 1 r. 12 p. 

2. Reduce 41.9682 square chains to acres. 

Ans. 4 ac. Or. 31 p. 

3. Reduce 132.925 square chains to acres. 

Ans. 13 ac. 1 r. 6.8 p. 

PROBLEM IV. 

To reduce acres, roods and perches to square chains. 

RULE. 

Divide the perches by 40 and prefix the roods ; divide 
the result by 4 and prefix the acres ; then this latter re- 
sult, multiplied by 10, will give the square chains. 

Or reduce the given quantity to perches and divide 
by 16. 

EXAMPLES. 

1. Reduce 13 ac. 1 r. 10 p. to square chains. 
40)10 



4)1.25 

13.3125 ,4=133.125 sg. ch. 



CHAP. I.] DIMENSIONS OF A SURVEY. 91 

2. Reduce 127 ac. 3r. 23 p. to square chains. 

Ans. 1278.9375 sq. ch. 

3. Reduce 35 ac. r. 20 p. to square chains. 

Ans. 351.25 sq. ch. 

PROBLEM V. 

To find the hearing of a line. 

1. Let a stake of six or eight feet in length be set up 
perpendicularly, at the far end of the line. Set up the 
compass staff perpendicularly, at the beginning of the 
line, and placing the compass on the staff, adjust it to 
a horizontal position ; the ball and socket admitting a 
motion for that purpose. This position can be deter- 
mined with sufficient accuracy, by observing whether, 
when the compass is turned round, the ends of the 
needle remain at the same height above the face of the 
instrument. 

2. Turn the compass round so as to bring the south 
end of it towards the stake at the far end of the line 
Then applying the eye to the sight at the north end, 
move the compass gently round till the stake can be 
seen through the fine slits in both sights, and let it re- 
main in this position. 

3. When the needle has settled, observe the number 
of degrees and parts of a degree, that are intercepted 
between the south end of the needle and the north or 
south point of the compass, to whichever it is nearest ; 
which will be the bearing, reckoning it from that point, 
towards the east if the south end of the needle is to the 
Tight hand, but towards the west if it is to the left hand 

Note 1. — The bearing thus obtained may be, and 
should be, verified by going to the far end of the line, 



92 DIMENSIONS OF A SURVEY. [CHAP. I. 

and from thence taking the bearing to the first end ; 
which, if both bearings are correct will be the reverse 
of the former. 

Note 2. — When there is a fence on the side, or other 
obstacle in the way, preventing the stake at one end 
from being seen through the compass sights at the other 
end, the bearing may be obtained by setting up the 
compass and stake at small equal distances to the right 
or left, so that the line joining them may be parallel to 
the side. 

Note 3. — The method of obtaining the bearing between 
two stations when there are obstacles in the way, which 
also prevent a parallel bearing being readily taken, or 
when the stations are too distant to be seen from each 
other, will be noticed in the next chapter. 

PROBLEM VI. 

To measure the distance of a line. 

For convenience in marking the termination of the 
chain in measuring, ten iron pins should be provided, 
about a foot in length, and terminated at top by a small 
ring, to which a piece of red flannel or other conspicuous 
substance should be tied, in order that the pins may 
be readily found, when set up among high grass or in 
other situations where they would not otherwise be 
easily discovered. 

Let the person who is to go foremost in carrying the 
chain, take nine of the pins in his left hand, and one end 
of the chain and the other pin in his right hand ; then he 
moving on in the direction of the line, let another person 
take the other end of the chain and hold it at the begin- 
ning of the line. When the leader has moved on till the 
chain is stretched tight, he must set down the pin, per- 



CHAP. I.] DIMENSIONS OF A SURVEY. 93 

pendicularly, exactly at the end of the chain, the hinder 
chain-man taking care that the chain is in the direction 
of the line ; which is readily determined by observing 
whether it is in a range with a stake previously set up 
at the far end of the line. When the leader has not his 
end of the chain in the direction of the line, the hinder 
chain-man can direct him which way to move, by a mo- 
tion of his left hand. When the distance of one chain 
or half chain* has been thus determined, the carriers, 
taking hold of the two ends of the chain, move on till 
the hinder one comes to the pin which was set up by the 
other ; then the chain being stretched, the person at the 
fore end of it sets up another pin as before ; the hinder 
chain-man then taking up the pin at his end, they proceed 
to a third distance of the chain ; and so on. When the 
person at the fore end of the chain has set up all his 
pins, he still moves on another length of the chain, 
and then setting his foot on it to keep it in place, he 
cries " out'' 1 The hinder chain man then comes forward, 
and counts to him the ten pins ; and he setting up one 
of them at the end of the chain, again moves on, drag- 
ging the chain after him, till he is checked by the hinder 
chain-man, who, getting the hind end of the chain, applies 
it as before to the pin set up. The number of outs 
should be carefully noticed ; each out being ten chains, 
when a four-pole chain is used, but only five, when the 
measuring is done, with a two-pole chain. When arri- 
ved at the end of the line, the number of pins, which the 
one at the fore end of the chain has set up since the last 
out, and the number of links from the last pin to the end 
of the line, must be carefully noted. From these, and 



* When a two-pole chain is used, one length of it may properly be called 
a half chain. 



94 



DIMENSIONS OF A SURVEY. 



[chap. 



the number of outs, the distance measured is readily 
determined. 

All slant or inclined surfaces, as the sides of a hill, 
should be measured horizontally, and not on the plane 
yr surface of the hill. To effect this, the hind end of 
the chain, in ascending a hill, should be raised from 
the ground till it is on a level with the fore end, and, by 
means of a plummet and line, or when the hill is not very 
steep, by estimation, should be held perpendicularly above 
the termination of the preceding chain. In descending 
a hill, the fore end of the chain should be raised in the 
same manner, and the plummet being suspended from 
it will show the commencement of the succeeding chain. 

PROBLEM VII. 

To protract a Survey, having the hearings and distances 
of the sides given. 
The method of doing this will be best understood by 
an example. Thus, 

Suppose the following field notes to be given, it is re- 
quired to protract the survey. 

Fig. 75. 










Ch. 


1. 


N. 


50° E. 


9.60 


2. 


S. 


32° E. 


16.38 


3. 


s. 


41° W. 


6.30 


4. 




West 


8.43 


5. 


N. 


79° W. 


10.92 


6. 


N. 


5° E. 


11.25 


7. 


8. 


83° E. 


6.48 



Method 1st, 
Draw NS, Fig. 75, to 
represent a meridian 
line; then N stand- 
ing lor the north and 



CHAP. I.] DIMENSIONS OF A SURVEY. 95 

S for the south, the east will be to the right hand, and 
the west to the left. In NS take any convenient point 
as A for the place of beginning, and apply the straight 
edge of the protractor to the hue, with the centre to 
the point A, and the arch turned towards the east, be- 
cause the first bearing is easterly; then holding the 
protractor in this position, prick off 50° the first bear- 
ing, from the north end, because the bearing is from 
the north ; through this point and the point A, draw 
the line AB on which lay 9.60 chains, the first distance 
from A to B. Now apply the centre of the protractor 
to the point B, with the arch turned toward the east, 
because the second bearing is easterly, and move it till 
the line AB produced, cuts the first bearing 50° ; the 
straight edge of the protractor will then be parallel to 
the meridian NS ; hold it in this position, and from the 
south end prick off the second bearing 32° ;' draw BC 
and on it lay the second distance 16.38 chains. Pro- 
ceed in the same manner at each station, observing 
always, previous to pricking off the succeeding bearing, 
to have the arch of the protractor turned easterly or 
westerly, according to that bearing, and to have its 
straight edge parallel to the meridian ; this last may 
always be done by applying the centre to the station 
point, and making the preceding distance line produced 
if necessary, cut the degrees of the preceding bearing. 
It may also be done by drawing a straight line through 
each station, parallel to the first meridian. 

When the survey is correct, and the protraction 
accurately performed, the end of the last distance will 
fall on the place of beginning. 

Method 2d. 
With the chord of 60° describe the circle NESW 



96 



DIMENSIONS OF A SURVEY. 



[CHAP. I. 



Fig. 76, and draw the diameter NS. Take the several 
bearings from the line of chords, and lay them off on 
the circumference from N or S according as the bearing- 
is northerly or southerly, and towards E or W accord- 
ing as it is easterly or westerly, and number them 1, 2. 
3, 4, &c, as in the figure. From A, the centre of the 
circle, to 1 draw A 1, on which lay the first distance 
from A to B ; parallel to A 2 draw BC, on which lay 
the second distance from B to C ; parallel to A 3 draw 
CD, on which lay the third distance from C to D ; pro- 
ceed in the same manner with the other bearings and 
distances. 



Fig. 76. 



i__..6 



EXAMPLE 2. 

The following field 




nc 


)tes are j 


^iven, to 


protract the 


survey. 






Ch. 


1. 


N. 15° 00' 


E. 20 


2. N. 37° 30' 


E. 10 


3. 


East 


7.50 


4. 


S. 11° 00' 


E. 12.50 


5. 


South 


13.50 


G. 


West 


10. 


7. 


S. 36° 30' W. 10. 


8. N. 38° 15' 


W. 8.50 



PROBLEM VIII. 

The bearing of two lines from the same station being 
given, to find the angle contained between them. 



RULE. 



When they run from the same point of the compass, 
towards the same point, subtract the less from the 
greater. 



CHAP. I.] DIMENSIONS OF A SURVEY. 



97 



When they run from the same point, towards different 
points, add them together. 

When they run from different points, towards the 
same point, add them together, and take the supple- 
ment of the sum. 

When they run from different points, towards different 
points, subtract the less from the greater, and take the 
supplement of the remainder. 

Note. — When the bearing of one of the lines is given 
towards the station, instead of from it, take the reverse 
bearing of such line ; the angle may then be found by 
the above rule. 



Fig. 67. 




EXAMPLES. 

1. Given the bearing of the line 
AB, Fig. 67, N. 34° E., and AD, 
N. 58° E. ; required the angle A. 

AD, N. 58° E. 
AB, N. 34° E. 

Angle A =24° 



2. Given the bearing of BA, Fig. 57, S. 34° W., and 
BC, S. 3.5° E. ; required the angle B. Ans. B = 69°. 

3. Given the bearing of BC, Fig. 67, S. 35° E., and 
CD, S. 87° W. ; required the angle C. Ans. 58°. 

4. Given the bearing of DC, Fig. 67, N. 87° E., and 
DA, S. 58° W.; required the angle D. Ans. 151°. 

9 N 



98 DIMENSIONS OF A SURVEY. [CHAP. *• 

PROBLEM IX. 

To change the bearings of the sides of a survey in a cor- 
responding manner, so that any particular one of them 
may become a Meridian. 

RULE. 

Subtract the bearing of the side that is to be made a 
meridian, from those bearings that are between the same 
points that it is, and also from those that are between 
points directly opposite to them. If it is greater than 
either of the bearings from which it is to be subtracted, 
take the difference, and change E. to W., or W. to E. 

Add the bearing of the side which is to be made a 
meridian, to those bearings which are neither between 
the same points that it is, nor between the points that 
are directly opposite to them. If either of the sums ex- 
ceeds 90°, take the supplement and change N. to S., or 
S. to N * 

Note. — When the bearings of some, or all, of the sides 
of a survey have been thus changed, and by calculation 
the changed bearing of another side or line has been 



* The changing of the bearings so as to make a given side become a 
meridian, may be illustrated by means of a protracted survey. If a pro- 
tracted survey or plot is held horizontally, with the meridian in a north 
and south direction, the north end being towards the north, the bearings 
of the sides of the plot will then correspond with the bearings of tin' sides 
of the survey. If then, keeping the paper horizontal, it be turned round 
till any particular side of the plot has a north and south direction, or be- 
comes a meridian, the bearings of all the other sides of the plot will have 
been changed by a like quantity. But it is evident, that neither the 
relation of the different parts of the plot to one another, the area nur 
the lengths of the sides will have been altered by this change. It may 
be here observed, that some calculations in surveying are considerably 
shortened by changing the bearings so as to make a certain side become 
a meridian. The method was communicated to me by Robert Patterson, 
late Professor of Mathematics and Natural Pliilosophy in tlic University 
of Pennsylvania. 



CHAP. I.] DIMENSIONS OF A SURVEY. 99 

found, its true bearing will be obtained by applying to 
the changed bearing, the bearing of the side which 
was made a meridian, in a contrary manner to what 
is directed in the rule ; that is, by adding in the case 
in which the rule directs to subtract, and by subtract- 
ing in the case in which it directs to add. 

EXAMPLES. 

1. Given the bearings of the sides of a survey as fol- 
low; 1st. S.45*°W.; 2d.N. 50° W.; 3d. North; 4th. 
N. 85° E.; 5th. S. 47° E.; 6th. S. 20i° W.; and 7th. N. 
51 1° W. Required the changed bearings, so that the 
5th side may be a meridian. 

1st, S. 45J°W. 

47 

92£ 
180 



chang. 


bear. 


N. 871 


° W. 


2d. 




N. 50° 
47 


w. 


chang, 


, beai 


•. N. 3° 


w. 


3d. 




N. 0° 

47 


E. 



chang. bear. N. 47° E. 
4th. N. 85° E. 

47 



132 
180 



chang. bear. S. 48° E. 



100 DIMENSIONS OF A SURVEY. [CHAP. 

5th. side, changed bearing, South. 

6th. S. 20i° W. 

47 



chang. bear. S. 67£ 

7th. N. 51° W. 
47 



chang bear. N. 4k W. 

2. Given the following bearings of the sides of a sur- 
vey ; 1st. S. 40i° E. ; 2d. N. 54° E. ; 3d. N. 29F E.; 4th. 
N. 281° E. ; 5th. N. 57° W. ; and 6th. S. 47° W. ; to find 
the changed bearings so that the 2d. side may be a me- 
ridian. Ans. 1st. N. 85^ E.; 2d. North; 3d. N. 241° W. ; 
4th. N. 25i° W. ; 5th. S. 69° W. ; 6th. S. 7° E. 

3. Given the bearings as in the 1st. example ; viz. 1st. 
S.45i°W.; 2d.N.50°W.; 3d. North; 4th. N. 85° E.; 
5th. S. 47° E. ; 6th. S. 201° W ; 7th. N. 5H° VV. ; to find 
the changed bearings so that the 6th side may be a me- 
ridian. Ans. 1st. S. 25° W. ; 2d. N. 70*° W. ; 3d. N. 
20i° W. ; 4th N. 64*° E. ; 5th. S. 67i° E. ; 6th. South ; 
7th. N. 711° W. 

PROBLEM X. 

Of the bearing. Distance, Difference of Latitude and De- 
parture, any two being given, to find the other two. 

RULE. 

Wlien the bearing and distance are given. 

As Rad. : cos. of bearing ; : distance : dif. of latitude. 
Rad. : sin. of bearing : : distance ; departure. 



CHAP. I.] DIMENSIONS OF A SURVEY. 101 

When the bearing and difference of latitude are given. 

As Rad. : sec. of bearing : : diff. lat. : distance. 
Rad. : tang, of bearing : : diff. lat. : departure. 

When the bearing and departure are given. 

As Rad. : cosec. of bearing : : departure : distance. 
Rad. :cotang. of bearing : : departure : diff. lat. 

When the difference of latitude and the departure are given. 

As diff. lat. : departure : : rad. : tang, of bearing. 
Rad. : sec. of bearing : : diff. lat. : distance. 

When the distance and difference of latitude are given. 

As Diff. lat. : distance : : rad. : sec. of bearing. 
Rad. : tang, of bearing : : diff. lat. : departure. 

When the distance and departure are given. 

As Distance : departure : : rad. : sin. of bearing. 
Rad. : cos. of bearing : : distance : diff. lat. 

Note. — It is evident the above proportions are the solu- 
tions of a right-angled triangle, having for its sides the 
distance, difference of latitude, and departure. 

EXAMPLES. 

1. Given the bearing of a line, N. 53° 20' E., distance 
13.25 ch. ; to find the difference of latitude and the de- 
parture. Ans. Diff. lat. 7.91 N. : dep. 10.63 E. 

9* 



102 DIMENSIONS OF A SURVEY. [CHAP. I. 

2. Given the bearing of a line, S. 32° 30' E., and the 
departure 10.96 ch. to find the distance and difference 
of latitude. Ans. Dist. 20.40 ch. ; diff. lat. 17.20 S. 



3. Given the distance of a line, running between the 
north and east, 44 ch. and its difference of latitude 34.43 
ch. ; to find the bearing and departure. 

Ans. Bearing, N. 38° 30' E. ; dep. 27.39 ch. E. 

4. The bearing of a line S. 32° 30' E., and the differ- 
ence of latitude 17.21 ch. being given, to find the dis- 
tance and departure. Ans. Dist. 20.41 ch.; dep. 10.96 E. 

5. Given the difference of latitude of a line 27.92 N., 
and the departure 5.32 E. ; to find the bearing and dis- 
tance. Ans. Bearing, N. 10° 47' E. ; dist. 28.42. 

6. The distance of a line, running between the north 
and west, is 35.35 ch., and its departure 15.08 ch., re- 
quired the bearing and difference of latitude. 

Ans. Bearing N. 25° 15' W.; diff. lat. 31.97 N. 

PROBLEM XI. 

To find the difference of latitude and departure correspond- 
ing to any given bearing and distance, by means of the 
Traverse Table. 

RULE. 

When the distance is any number of whole chains or 
perches, not exceeding 100. 

Find the given bearing at the top or bottom of the table, 
according as it is less or more than 45°. Then against 



CHAT. I. J DIMENSIONS OF A SURVEY. 103 

the given distance, found in the column of distances at 
the side of the table, and under or over the given bearing, 
is the difference of latitude and departure ; which must, 
be taken as marked at the top of the table, when the 
bearing is at the top; but as marked at the bottom, 
when the bearing is at the bottom. 

When the distance is a number of whole chains or perches, 
exceeding 100. 

Separate the distance into parts that shall not exceed 
100 each; and find, as before, the difference of latitude 
and departure, corresponding to the given bearing and 
to each of those parts ; the sums of these will be the dif 
ference of latitude and departure required. 

When the distance is expressed by chains or perches and 
the decimal of a chain or perch. 

Find, as above, the difference of latitude and departure 
corresponding to the given bearing and to the whole 
chain or perches. Then considering the decimal part 
as a whole number, find the difference of latitude and de- 
parture corresponding to it, and remove the decimal 
point in each of them, two figures to the left hand if there 
are two decimal figures in the distance, or one figure to 
the left if there is but one ; then these added to the 
former will give the difference of latitude and departure 
required. 

Note. When the number of whole chains or perches 
is less than 10, and the second decimal figure is a cipher, 
the difference of latitude and departure may be taken 
out at once, by considering the mixed number, rejecting 



104 DIMENSIONS OF A SURVEY. [CHAP. I. 

the cipher, as a whole number. The difference of lati- 
tude and departure thus found, must have the decimal 
point in each, removed one figure to the left hand. 



EXAMPLES. 

1. Given the bearing of a line S. 35i° E., dist. 79 ch. ; 
required the difference of latitude and departure by the 
traverse table. Ans. Dim lat. 64.51 S. ; dep. 45.59 E. 

2. A line bears N. 20£° E., 117 ch. ; required the dif- 
ference of latitude and the departure. 

Dist. 100, gives diff. lat. 93.67 and dep. 35.02 
17 15.92 5.95 



Whole dist. 117 diff. lat. 109.59 N. dep. 40.97 E. 

3. Required the difference of latitude and the de- 
parture of a line which bears, S. 411° W., 57.36 ch. 

Dist. 57.00 gives diff. lat. 42.53 and dep. 37.96 
36 .27 .24 



Whole dist. 57.36 diff. lat. 42.80 S. dep. 38.20 W. 

4. Required the difference of latitude and departure 
of a line which bears, N. 72° W., 124.37 ch. 

Dist. 100.0 gives diff. lat. 30.90 and dep. 95.11 

24.00 7.42 22.83 

.37 .11 .35 



Whole dist. 124.37 diff. lat. 38.43 N. dep. 1 18.29 W. 



CHAP. I.] DIMENSIONS OF A SURVEY. 105 

5. Given the bearing and distance of a line, N. 392° 
W. 15.20 ch., to find its difference of latitude and de- 
parture. Am. Diff. lat. 11.72 N., and dep. 9.67 W. 

6. The bearing and distance of a line are N. 46° E., 
27.25 ch. ; required its difference of latitude and de- 
parture. Am. Diff. lat. 18.93 N. and dep. 19.60 E. 

7. The bearing and distance of a line are S. 37£° W., 
137.50 ch. ; required its difference of latitude and de- 
parture. Am. Diff. lat. 109.45 S., and dep. 83.23 W. 

8. Required the difference of latitude and departure 
of a line, whose bearing and distance are S. 6£° E., 
5.60 ch. Am. Diff. lat, 5.56 S., and dep. 0.63 E. 



PROBLEM XII. 

Given the beatings and distances of all the sides of a tract 
of land to obtain the corrected latitudes and departures. 

RULE. 

1. Rule a table as in the annexed example, in the first 
vertical column of which, place the letters designating 
the sides, or the numbers denoting the stations at the be- 
ginning of each side ; in the second column, place the 
bearings ; and, in the third, the distances. 

2. Find, by the last problem, the difference of latitude 
and the departure, corresponding to each side, and place 
them in the next four columns, under their proper heads 
of N. or S., E. or W. Add up the northings and south- 
ings ; and if the sums are not equal, find their difference ; 

O 



106 DIMENSIONS OF A SURVEY. [CHAP. I. 

which will be the error of the survey in difference of 
latitude ; which call by the same name as the least sum. 
Proceed in the same manner with the eastings and west- 
ings, and find the error in departure. Also add up the 
column of distances. Then it will be, 

As the sum of the distances, 
Is to any particular distance, 
So is the error in latitude or departure 
To the correction of latitude or departure, correspond- 
ing to that distance. 

3. Find, by the above proportion, the corrections of 
latitude and departure corresponding to all the sides 
calculating them to the nearest two decimal figures, and 
place them in the next two columns, heading them with 
the same names as the errors in latitude and departure. 
If the sums of these corrections, are not respectively 
equal to the errors in latitude and departure, which, in 
consequence of the fractions neglected, will sometimes 
be the case, alter some of them by a unit in the second 
decimal figure, to make them so. 

4. Apply these corrections to their corresponding dif- 
ferences of latitude and departures, by adding when of 
the same name, but by subtracting w r hen of different 
names, and the corrected differences of latitude and de- 
partures will be obtained ; which may be placed in the 
four succeeding columns. 

In these the sums of the northings and southings will 
be equal, and also those of the eastings and westings.* 



* The directions given in the rule, for correcting the errors in difference 
of latitude and departure, are deduced from the rule given and demonstrated 
in No. 4, of a periodical work, called the Analyst, by Nathaniel Bowditch, 
A. M., and also by the editor, Professor Adrain. The demonstration is too 
long, and not of a nature for insertion here. 



CHAP. I.] 



DIMENSIONS OF A SURVEY. 



107 



Note 1. — In the proportion for finding the correction of 
the latitude or departure, the decimal parts of the sura 
of the distances and of the particular distance may be 
omitted, taking, in each case, the nearest number of whole 
chains. 

2. The corrections may be frequently estimated with 
sufficient accuracy without the trouble of working out 
the proportions. 

3. When one or two of the sides are hilly, or when 
there are other difficulties in the way of obtaining their 
bearing or distances with accuracy, it is better to allow 
a considerable part of the errors, on the latitudes and de- 
partures corresponding to them, and afterwards to ap- 
portion the remaining part among the others. 

EXAMPLES. 

1. Given the bearings and distances of the sides of a 
tract of land as follow : 1st. S. 404° E. 31.80 ch. ; 2nd. 
N. 54° E. 2.08 ch.; 3rd. N. 29i° E. 2.21 ch.; 4th. N. 
281° E. 35.35 ch. ; 5th. N. 57° W. 21.10 ch.; 6th. S. 47° 
W. 31.30 ch. Required the corrected differences of 
latitude and departures. 



Sta. 


Courses. 


Dist. 
Ch. 


N. L. 


S.L. 


E. D. 


W.D. 


Cor. 
S. 


Cor. 
E. 


N.L. 


S. L. 


E. D 


W.D. 


1 


S. 40 a E. 


31.80 




24.18 


20.65 




.03 


.05 




24.2120.70 




2 


N. 54 E. 


2.08 


1.23 




1.68 




.00 


.00 


1.23 




1.68 




3 

4 


N.291E. 


2.21 


1.92 




1.08 




.00 


.00 


1.92 




1.08 




N.28|E. 


35.35 


31.00 




17.00 




.04 


.05 


30.96 




17.05 




5 


N. 57 W. 


21.10 


11.49 






17.69 


.02 


.03 


11.47 


1 
f 


17.66 


6 


S.47.W. 


31.30 




21.34 




22.89 


.03 


.04 




21.37 




22.85 






123.84 


45.64 
45.52 


45.52 


40.41 


40.58 
40.41 


.12 


.17 


45.58 


45.58 


40.51 


40.51 



12 Er. S. 



.17 Er. E. 



108 



I 




DIMENSIONS OF 


A SURVEY. 




[chap, 


As 124 


: 32 : 


: .12 : .03 


As 124 : 32 : : 


.17 : 


.04 or .05* 


124 


: 2 : 


: .12 : .00 




124 : 2 : : 


.17 : 


.00 


24 : 


35 : 


: .12 : .03 or .04 




124 : 35 : : 


.17 : 


.05 


124 


: 21 : 


: .12 : .02 




124 : 21 : : 


.17 : 


.03 


124 : 


31 : 


: .12 : .03 




124 : 31 : : 


.17 : 


.04 



2. Given the bearings and distances of the sides of a 
tract of land as follow: 1st. N. 75° E. 13.70 ch.j 2d. 
N. 20i E. 10.30 ch.; 3d. East 16.20 ch. ; 4th. S. 33*° 
W. 35.30 ch. ; 5th. S. 76 W. 16 ch. ; 6th. North 9 ch. ; 
7th. S. 84° W. 11.60 ch.; 8th. N. 53^° W. 11.60 ch. ; 
9th. N. 361° E. 19.36 ch.; 10th. N. 22*° E. 14 ch. ; 11th. 
S. 761° E. 12 ch.; 12th. S. 15° W. 10.85 ch. ; 13th. S. 
18° W. 10.62 ch. ; to the place of beginning. Required 
the corrected latitudes and departures. 

Ans. 1st. 3.56 N. 13.26 E. ; 2d. 9.66 N. 3.62 E. ; 

3d. 0.02 N. 16.22 E. ; 4th. 29.39 S. 19.44 

W.j 5th. 3.8'5 S. 15.50 W. ; 6th. 9.01 N. 

0.01 E. ; 7th. 1.19 S. 11.52 W. ; 8th. 6.96 

N. 9.27 W. ; 9th. 15.54 N. 11.61 E. ; 10th. 

12.95 N. 5.38 E. ; 11th. 2.73 S. 11.70 E. ; 

12th. 10.46 S. 2.80 W.; 13th. 10.08 S. 

3.27 W. 



* When, as in this case, the correction is found to be nearly midway be- 
tween two numbers, it is best to note them both. Then, if in using the one 
that is nearest to the true value, the sum of the corrections does not equal 
the whole error, the other should be taken. 



CHAP. II. J SUPPLYING OMISSIONS. 109 



CHAPTER H. 

On supplying omissions in the dimensions of a survey. 

When the bearings and distances of all the sides of a 
survey are known, except one bearing and one distance, 
or two bearings, or two distances, these can be obtained 
by calculation, provided those that are known can be 
depended on, as sufficiently accurate. This may some- 
times be necessary when there are obstacles in the way 
of obtaining one or two of the bearings or distances ; or 
when, after they have all been taken on the ground, the 
notes of one or two of them happen to be obliterated. 
As, however a bearing, or distance thus obtained, must 
be affected by any error or errors that may have been 
made in taking the others, it is better, when practicable, 
to have the bearings and distances of all the sides, as 
taken on the ground. 

PROBLEM I. 

The bearings and distances of all the sides of a tract of 
land, except the bearing and distance of one side, being 
given, to find these. 

RULE. 

Find by prob. 11, of the preceding chapter, the differ- 
ences of latitude and the departures for the sides whose 
bearings and distances are given, and place them in 
their proper columns in a table ruled for the purpose : 
Add up the northings and southings, and taking the dif- 
10 



110 SUPPLYING OMISSIONS. [CHAP. II. 

ference of their sums, place it opposite the unknown 
side, in the column whose sum is the least. The sums 
of the two columns will then be equal. This is called 
balancing the latitudes. Do the same with the eastings 
and westings. The two numbers inserted to make the 
latitudes and the departures balance, will be the differ- 
ence of latitude and the departure of the unknown side : 
with which its bearing and distance may be found, by 
prob. 10, of the preceding chapter. 

Note 1. — By the application of this rule, the bearing 
and distance of a line joining two corners or stations, 
may be found, when there are obstacles in the way which 
prevent our going directly from one corner to the other, 
or when one cannot be seen from the other. To do this, 
let one or two, or more stations, if necessary, be taken 
out of the line, and take the bearing and distance from 
the first corner to the first assumed station ; from this 
station to the second ; and so on, to the second corner. 
Then considering these bearings and distances, as the 
bearings and distances of the sides of a survey, the re- 
quired bearing and distance of the line may be found by 
the above rule. The bearing thus found must be revers- 
ed, in order to have the bearing from the first corner to 
the second. 

2. In the same way the bearing and distance of a 
straight road to run between two given places, may be 
found, by taking the several bearings and distances of 
the old road if there is one ; or of lines joining assumed 
stations and extending from one of the places to the other. 

EXAMPLES. 

1. The bearings and distances of the side of a tract of 
land, except the bearing and distance of one side which 



CHAP. II. J SUPPLYING OMISSIONS. Ill 

are not known, are as in the following field-notes ; re- 
quired the unknown bearing and distance. 



Chains. 

1. S. 45°^ W. 15.16 

2. N. 50° W. 22.10 

3. North 18.83 

4. N. 85° E. 35.65 



Chains. 

5. 

6. S. 20* W°. 23.80 
7 N. 5H W°. 26.47 



Sta. 


Bearings. 


Dist 


N. 


s. 


E. 


w. 


1 


S. 45i W. 


15.16 




10.62 




10.81 


2 


N. 50 W. 


22.10 


14.20 






16.93 


3 


North 


18.83 


18.83 








4 


N. 85 E. 


35.65 


3.11 




35.52 




5 








(19.79) 


(21.20) 




6 


S. 20i W. 


23.80 




22.29 




8.33 


7 


N. 51i W. 


26.47 


16.56 






20.65 








52.70 


52.70 


56.72 


56.72 



Asdiff. oflat. 19.79 S. 
: dep. 21.20 E. 

: : rad. - - - - - 

: tang. bear. S. 47° E. 



Ar. Co. 8.70355 

■ - - 1.32674 

■ - - 10.00000 



As rad. - - - - 
: sec. bearing 47° - 
: : diff. lat. 19.79 



10.03029 

10.00000 

10.16622 

1.29645 



: dist. - - 29.02 - 

Ans. S. 47° E. 



- - - 1.46267 
29.02 ch. 



112 SUPPLYING OMISSIONS. [CHAP. II. 

2. Given the bearings and distances of the sides of a 
tract of land, as follow: 1st. N. 15f W 9.40 ch.; 2dN. 
632 E. 10.43 ch. ; 3d. S. 49° E. 8.12 ch. ; 4th. S. 13* E. 
8.45 ch. ; 5th. S. 161 E. 6.44 ch. ; 6th. Unknown j 7th. N. 
60° W. 9.72 ch. j 8th. N. 17i E. 7.65 ch.; required the 
bearing and distance of the 6th. side. 

Arts. S. 60° 8' W. 12.27 ch. 

3. One side of a tract of land of which a survey is to 
be taken, passes through a pond. Two stations are 
therefore taken on one side of the pond as represented 
in Fig. 80. The bearings and distances from the first 
end of the side to the first station, from that to the second, 
and thence to the other end of the side are; 1st. S. 
52° W. 10.70 ch. ; 2d. S. 1\° W. 13.92 ch. ; and 3d. S. 
34« E. 9 ch. Required the bearing and distance of the 
side. Am. S. 10° 33' W. 28.31 ch. 

4. Given the bearings and distances of an old road, 
running between two places, as follow; 1st. S. 10° E. 
92.20 ch.; 2d. S. 15° W. 120.50 ch. ; 3d. S. 184 W. 
205. ch. ; 4th. S. 714 E. 68 ch. Required the bearing 
and distance of a straight road, that shall connect the 
two places. Ans. S. 2° 8' W. 423.47 ch. 

PROBLEM H. 

Given all the bearings and distances of the sides of a sur- 
vey, except the distances of two sides, to find these. 

RULE. 

By prob. 9, of the preceding chapter, change all the 
given bearings, in a corresponding manner, so that one 
of the sides whose bearings only are given, may become 
a meridian. With the changed bearings and given dis- 
tances find the corresponding differences of latitude, and 
the departures. Add up the eastings and westings, 
and take the difference of their sums, which will be the 



SUPPLYING OMISSIONS. 



113 



CHAP. II.] 

departure of that unknown side, which is not made a me- 
ridian. With this departure and the changed bearing, 
find by prob. 10, of the preceding chapter, the distance 
and difference of latitude of this side, which place in 
their proper columns. Now add up the northings and 
southings, and take their difference, which will be the 
distance of the side made a meridian.* 



EXAMPLES. 



Given the following bearings and distances of the 
sides of a survey; lst.S. 45i W. 15.16 ch. ; 2d.N. 50° 
W. 22.10 ch. ; 3d. North 18.83 ch. ; 4th. N. 85° E. 35.65 
ch. ; 5th. S. 47° E. dist. unknown; 6th. S. 20| W. dist 
unknown ; 7th. N. 51i W. 26.47 ch. to the place of be- 
ginning. Required the unknown distances. 



Sta. 


Bearings. 


Changed 

bearings. 


Dist. 


N. 


S. 


E. 


W. 


1 


S. 451° W. 


N. 87i° W. 


15.16 


0.66 






15.15 


* 


N. 50 W. 


N. 3 W. 


22.10 


22.07 






1.16 


3 


North 


N. 47 E. 


18.83 


12.85 




13.77 




4 


N. 85 E. 


S. 48 E. 


35.65 




23.85 


26.49 




5 


S. 47 E. 


South 


(29.02) 




(29.02) 






6 


S. 20j W. 


S. 67i W. 


(23.80) 




(9.11) 




(21.99) 


7 


N. 51i w. 


N. 4^W. 


26.47 


26.40 






1.96 




1 


61.98 


61.98 


40.26 


40.26 1 



* The reason of the rule is obvious. For as the side made a meridian has 
no departure, the difference of the sums of the departures, must be the de- 
parture of the other unknown side. And when the difference of latitude of 
this side has been found and placed in its proper situation, the difference of 
the sums of the latitudes must evidently be the difference of latitude of the 
side made a meridian ; or which, in this case, is the same thing, its distance- 

10* p 



114 SUPPLYING OMISSIONS. [CHAP. II. 

Asrad. 10.00000 

: cosec. chang. bearing 67i° - - 10.03438 
: : dep. 21.99 1.34223 

: Dist. 6th side - - 23.80 - 1.37661 

Asrad. 10.00000 

: cotang. chang. bearing 67£ - - 9.61722 
: : dep. ------ 21.99 - 1.34223 

: diff. lat. 6th. side - - 9.11 - 0.95945 
Ans. 5th. side 29.02 ch. and 6th. side 23.80 ch. 

2. Given the bearings and distances of a tract of land 
as follow: 1st. S. 40i E. 31.80 ch.; 2d. N. 54° E. dist. 
unknown ; 3d. N. 29* E. 2.21 ch. ; 4th. N. 281 E. 35.35 
ch. ; 5th. N. 57° W. dist. unknown ; 6th. S. 47° W. 31.30 
ch. ; to the place of beginning. Required the distances 
of the 2d. and 5th. sides. 

Ans. 2d. side. 2.08 ch. and 5th. side 20.90 ch. 



PROBLEM III. 

Given the bearings and distances of all the sides of a sur- 
vey except two ; one of which has only its bearing given, 
and the other, the distance and the points of the compass 
between which it runs ; to find the unknown bearing and 
distance. 



As in the last problem, change all the given bearings, 
so that the side whose bearing only is given, may be- 
come a meridian. Find the differences of latitude and 
the departures, corresponding to the changed bearings 
and the given distances. Take the difference of the 
sums of the eastings and westings, which will be the de- 



CHAP. II.] SUPPLYING OMISSIONS. 115 

parture of the side whose bearing is not given. With 
the given distance and this departure, find by chap. 1. 
prob. 10. the changed bearing and difference of latitude, 
and place them in their proper columns. From the 
changed bearing, the true bearing may be readily found 
by note to prob. 9. chap. 1. Lastly, take the difference 
of the sums of the northings and southings, and it will 
be the distance of the side, changed to a meridian. 

Note-. — The changed bearing as found by the rule, 
must be reckoned from the north, or the south point of 
the compass, according as the one, or the other, will ren- 
der the true bearing when found from it, conformable to 
the given points. The point from which the changed 
bearing must be reckoned determines also the column in 
which the difference of latitude must be placed. Some- 
times the changed bearing when reckoned from either 
north or south, will render the true bearing conformable 
to the given points. In such cases, there are two differ- 
ent bearings and distances that will answer the condi- 
tions of the problem ; and we can only know which of 
them is the right one by previously knowing the required 
bearing nearly. 

EXAMPLES. 

1. Given the bearings and distances of a survey as fol- 
low: 1st. S. unknown W. 15.16 ch.; 2d. N. 50° W. 
22.10 ch. ; 3d. N. 18.83 ch. ; 4th. N. 85° E. 35.65 ch. ; 
5th. S. 47° E. 29.02 ch.; 6th. S. 20$ W. dist. unknown; 
7th. N. 51i° W. 26.47 ch. Required the unknown bear- 
ing and distance. 



116 



SUPPLYING OMISSIONS. 



[CHAP. II. 



Sta. 


Bearings. 


Changed 
bearings. 


Dist. 


N. | S. 


E. j' YV. | 


1 

2 


S. (45° 36') W. 


(S. 25° 6' W.) 


15.16 


13.73 !(6.43) 


N. 50 W. 


N. 70i W. 


22.10 


7.37 j 


20.83 


3 


North 


N. 20£ W. 


18.83 


17.64 




6.59 


4 


N. 85 E. 


N. 64£ E. 


35.65 


15.35 




32.18 




5 


S. 47 E. 


S. 67i E. 


29.02 




11.11 


26.81 




6 


S. 20£ W. 


South 


(23.81) 




(23.81) 




25.14 


7 


N. 51i W. 


N. 71f W. 


26.47 


8.29 














48.65 


48.65 


58.99 


58.99 



As dist. 1st, side 15.16 
: dep. do. 6.43 

: : rad, ------ 



Ar. Co. 8.81930 

0.80821 

- - 10.00000 



sin. chan. bear. 25° 6' 



9.62751 



As rad. 10.00000 

: cos. chang. bearing 25° 6' - - 9.95692 
: : dist. 15.16 - - 1.18070 

: diff. lat. - - - - 13.73 - - 1.13762 
Ans. 1st. S. 45° 36' W. ; 6th. 23. 81 ch. 



2. Given the following bearings and distances of a 
survey: 1st. S. 40£° E. 31.80 ch. ; 2d. N. 54° E. dist. 
unknown 3rd. N. 29F E. 2.21 ch. j 4th. N. unknown E. 
35.35 ch.; 5th. N. 57° W. 20.90 ch.; 6th. S. 47° W. 
31.30 ch. ; to place of beginning. Required the bearing 
of the 4th. side and distance of the 2d. side. 

Ans, Bearing of 4th. side N. 285° E . ; dist. of 2d. 
side, 2.09 ch. 



CHAP. II.] SUPPLYING OMISSIONS. 117 

PROBLEM IV. 

Given all the bearings and distances of the sides of a tract 
of land, except the bearings of two sides, to find these 
bearings. 

RULE. 

1. Find the difference of latitude and the departure of 
each side, whose bearing and distance are both given. 
Take the difference of the sums of the northings and 
southings of these sides, and also the difference of the 
sums of the eastings and westings. These differences 
will be the difference of latitude, and the departure of a 
tine, which, with those sides, would form a closing survey; 
and which may therefore be called a closing line. 

2. With the difference of latitude and departure of 
the closing line, find, by prob. 10. chap. 1, its bearing and 
distance. Take the closing line and the two sides whose 
bearings are not given, for the three sides of a triangle, 
and calculate the angles. 

3. To the bearing of the closing line, apply, by addi- 
tion or subtraction, as the case may require, the angle 
contained between it, and the side which is the one 
coming first in the order of the survey ; and it will give 
the bearing of that side. Then to the reverse bearing 
of that side, apply in a proper manner, the angle con- 
tained between the two sides which are sides of the sur- 
vey, and it will give the bearing of the second of those 
sides.* 



* It is easy to see the reason of the rule, hy considering that the two sides 
whose bearings are not given, being made to form with the closing line, the 



118 



SUPPLYING OMISSIONS. 



[chap. II. 



EXAMPLES. 

1. Given the bearings and distances of the sides of a 
tract of land as follow : 1st. S. unknown W. 15.16 ch. ; 
2d. N. 50° W. 22.10 ch.; 3d. North 18.83 ch. ; 4th. N. 
85° E. 35.65 ch. ; 5th. S. unknown E. 29.02 ch. ; 6th S. 
201° W. 23.80 ch. ; and 7th. N. 51* W. 26.47. ch. Re- 
quired the unknown bearings. 



Sta. 


Bearings. 


Dist 


N. 


s. 


E. 


w. 


1 


s. w. 


15.16 










2 


N. 50° W. 


22.10 


14.20 






16.93 


3 


North 


18.83 


18.83 








4 


N. 85 E. 


35.65 


3.11 




35.52 




5 


S. E. 


29.02 










6 


S. 20* W. 


23.80 




22.29 




8.33 


7 


N. 5H W. 


26.47 


16.56 






20.65 








52.70 


22.29 


35.52 


45.91 



30.41 S. 



10.39 E. 



sides of a triangle, the sum or difference of their differences of latitude, will 
necessarily be equal to the difference of latitude of the closing line ; and that, 
therefore, their differences of latitude will be such as to make the sums of 
the northings and southings of the whole survey equal ; and the same for the 
departures. 



CHAP. II.] 



SUPPLYING OMISSIONS. 



119 



As diff. lat. 
: dep. 
: : rad. 



- 30.41 S. 

- 10.39 E. 



Ar. Co. 8.51698 

1.01662 

- - 10.00000 



: tang, of bear, of clos. line, S. 18° 52' 

As rad. 

: diff. lat. 30.41 

: : sec. of bear, of clos. line - 18° 52' 



dist. of clos. line 



32.14 



9.53360 

10.00000 

1.48302 

10.02398 

1.50700 




Let DE, Fig. 78, represent the 
closing line, DF, the 1st side of the 
survey, and FE, the 5th side. Then, 
DE 32.14 



DF 15.16 
FE 29.02 



2)76.32 



Half sum 38.16 



Rem. 6.02 
Cos. h F 43° 44 
F 



Ar. Co. 8.81930 
— 8.53730 



log. 1.58161 
— 0.77960 



28 



AsDE 
: FE 

: : sin. F 



32.14 

29.02 

87° 28' 



Ar. Co. 



2)19.71781 

9.85890 
8.49295 
1.46270 
9.99958 



sin. D 64° 26' 
DE, S. 18° 52' E. 
Angle D 64 26 



9.95523 
FD, N. 45° 34' E. 
Angle F 87 28 



1st side, S. 45 34 W. 



133 2 
180 00 



5th side, S. 46 58 E. 



120 CONTENT OF LAND. [CHAP. III. 

2. Given the bearings .and distances of the sides of a 
tract of land as follow: 1st. S. unknown E. 31.80 ch.; 
2d. N. 54° E. 2.08 ch.; 3d. N. 29i E. 2.21 ch.; 4th. N. 
281° E. 35.35 ch.; 5th. N. 57° W. 20.90 ch.; and 6th. S 
unknown W. 31.30 ch. to the place of beginning. Re- 
quired the unknown bearings. 

Am. 1st. S. 40° 29' E.: and 6th. S. 47° W. - 



CHAPTER III. 

Problems for finding the Content of Land. 

When the sides of a survey are right lines, and all the 
bearings and distances are given, the area may be found 
by a problem that will be given in this chapter. If one 
or two of the bearings or distances are not known, they 
may be found by the problems in the last chapter. Al- 
though the problem alluded to, is general, and may be 
applied whatever number of sides there may be, yet 
there are some particular rules for finding the areas of 
triangles and quadrilaterals, which are often useful. 
These, and also rules for finding the areas of circles 
and ellipses, are given in the first part of the chapter. 

When a part of the boundary of a tract of land, is 
irregular, as is frequently the case, if one or more of the 
sides are bounded by water, it is sometimes very trouble- 
some to take all the bearings and distances requisite to 
obtain the area with accuracy. In these cases, it is 
usual to run one or more straight lines, called stationary 
lines, near to such boundary, and so as to connect the 
straight sides of the survey. In measuring these sta- 
tionary lines, perpendicular distances are measured from 
them, to each bend in the irregular boundary. T1k's<' 
perpendicular distances are called off-sets. The lengths 



CHAP. III.] CONTENT OP LAND. 121 

of the off-sets, and the distance of the foot of each, from 
the commencement of the stationary line, should be care- 
fully noted in the field book ,• observing also that such a 
number of off- sets should be taken, that the part of the 
irregular boundary intercepted between each adjacent 
two, may, without material error, be considered a straight 
line. From these notes, the area or areas of the land 
contained between the stationary line or lines, and the 
irregular boundary, may readily be calculated. This 
area added to the area enclosed by the stationary lines, 
and straight sides of the survey, when they are on the 
outside of the stationary lines, or subtracted from it, 
when on the inside, will give the area of the survey. 

In those cases in which water is a boundary of a 
tract of land, if that water is a brook or rivulet, it is 
usual to consider a line running through its middle as 
the true boundary; and the off-sets mast be measured 
accordingly. When tide water is the boundary, the 
land is considered as extending to the line of low 
water mark. 

If the bearings of all the corners of a tract of land 
from two stations, taken either within or out of the tract 
are given, and also the bearing and distance of these 
stations from each other, the area may be calculated. 
It is however necessary, that the two stations should be 
so taken that they shall not be in a straight line, or very 
nearly in a straight line, with either of the corners of the 
land. This method of obtaining the area, though not 
practically so accurate as where the bearings and dis- 
tances of the sides are correctly given, may sometimes 
be found useful. 

Some surveyors, in order to calculate the area of a 
survey, first protract it ; then dividing the plot into tri- 
ll Q 



122 CONTENT OF LAND. [CHAP. III. 

angles and trapeziums by lines joining opposite corners, 
they measure with the scale and dividers the lengths of 
such lines and perpendiculars as are requisite for calcu- 
lating the areas of these. The sum of the areas thus 
obtained, is the area of the survey. When the survey 
is carefully protracted, and proper attention is given to 
take the measures with the utmost precision, this method 
serves to give a near value of the content ; but is by no 
means to be depended on as equally accurate with the 
general problems mentioned above. 

The area of a field or small tract of land, the corners 
of which can be seen from one another, may readily be 
found by means of the chain only. To do this, the lengths 
of the sides must be measured, and also the length of 
diagonals joining opposite corners, so as to divide the 
field into triangles. Or instead of the diagonals, the dis- 
tances from some assumed point within the field, to the 
several corners, may be used* Having then all the sides 
of the several triangles, the area of each may be found ; 
and the sum of these areas will be the area of the tract. 



PROBLEM I. 

To find the area of a Parallelogram, whether it be a Square, 
a Rectangle, a Rhombus, or a JShomboides, 

RULE. 

Multiply the length by the height or perpendicular 
breadth, and the product will be the area.* 



Fig. 68. * Demonstration. Let ABCD (Figs 68) be 

a rectangle; and let its length AB and CD, 
and its breadth AD and BC, be each divided 
into as many equal parts, as are expressed 
by the number of times they contain the 
B lineal measuring unit ; and let all the oppo- 
site points of division be connected by right 



D 

A 



CHAP. III. J CONTENT OF LAND. 123 

Note. — Because the length of a square is equal to 
its height, its area will be found by multiplying the side 
by itself. 

EXAMPLES. 

1. Required the area of a square field, a side of which 
measures 7.29 four-pole chains. 

7.29 Ch. 
7.29 



6561 
1458 
5103 



10)53.1441 Area 5 A. 1 R. 10 P. 

5.31441 
4 



1.25764 
40 

10.30560 



2. Required the area of a rectangular field whose 
length is 13.75 chains, and breadth 9.5 chains. 



lines. Then, it is evident that these lines divide the rectangle into a num- 
ber of squares, each equal to the superficial measuring unit ; and that the 
number of these squares is equal to the number of lineal measuring units in 
the length, as often repeated as there are lineal measuring units in the 
breadth, or height ; that is, equal to the length multiplied by the breadth. 
But the area is equal to the number of squares or superficial measuring units ; 
and therefore the area of a rectangle is equal to the product of the length 
and breadth. 

Again, a rectangle is equal to any oblique parallelogram of an equal length 
and perpendicular height (36.1;) therefore the area of every parallelogram 
is equal to the product of its length and height 



124 CONTENT OF LAND. [CHAP. in. 

13.75 Ch. 
9.5 



6875 
12375 



10)130.625 Area 13 A. OR. 10 P. 



13.0625 
4 



.2500 
40 

10.0000 
3. Required the area of a field, in the form of a rhom- 
boides, whose length AB is 42.5 perches, and perpen- 
dicular breadth CD is 32 perches. Fig. 15. 
42.5 P. 
32 

850 
1275 



4|0)136|0.0 
4)34 



8A. 2R. 

4. What is the area of a square tract of land whose 
side measures 176.4 perches? Ans. 194 A. 1 R. 36.96 P. 

5. What is the area of a rectangular plantation whose 
length is 52.25 chains, and breadth 38.24 chains ? 

Ans. 199 A. 3 R. 8.6 P. 

6. The length of a field, in the form of a rhombus, 
measures 16.54 chains, and the perpendicular breadth 
12.37 chains: required the area. Ans. 20 A. 1 R. 33.6 P. 



CHAP. III.] CONTENT OF LAND. 125 

7. Required the area of a field in the form of a rhom- 
boides, whose length is 21.16 chains, and perpendicular 
breadth 11.32 chains. Arts. 23 A. 3 R. 32.5 P. 

PROBLEM II. 

To find the area of a triangle when the base and perpen- 
dicular height are given. 

RULE. 

# 
Multiply the base by the perpendicular height, and 

half the product will be the area.* 

EXAMPLES. 

1. The base AB of a triangular piece of ground, 
measures 12.38 chains, and the perpendicular CD 6.78 
chains : required the area. Fig. 49. 

12.38 Ch. 

6.78 



9904 
8666 

7428 

2)83.9364 

10)41.9682 Area, 4 A. OR. 31 P. 

4.19682 
4 



.78728 
40 

31.49120 



* Demonstration. A triangle is half a parallelogram of the same base 
atid altitude, (41.1) and therefore the truth of the rule is evident. 
11* 



126 CONTENT OF LAND. [CHAP. III. 

2. Required the area of a triangular field, one side of 
which measures 18.37 chains, and the distance from this 
side to the opposite angle, 13.44 chains. 

Ans. 12 A. 1R. 15 P. 

3. What is the area of a triangle whose base is 49 
perches and height 34 perches ? Ans. 5 A. OR. 33 P. 

PROBLEM III. 

To find the area of a triangle when two sides and their 
included angle are given. 

RULE. 

As radius, 

Is to the sine of the included angle j 
So is the rectangle of the given sides, 
To double the area.* 



EXAMPLES. 

1. In a triangular lot of ground ABC, the side AB 
measures 64 perches, the side AC 40.5 perches, and 
their contained angle CAB 30°: required the area. 
Fig. 49. 



* Demonstration. In the triangle ABC, Fig. 49, let AB and AC be the 
given sides, including the given angle A, and let CD be perpendicular on AB. 
Then by trig. rad. : sin. A : : AC : CD; but (cor. 1.6) AC : CD : : ACx AB ; 
CDx AB; therefore (11.5) rad. : sin. A : : ACx AB : CDx AB ; but CD X 
AB is equal to twice the area of the triangle : hence the truth of the rule is 
evident 



CHAP. III.] CONTENT OP LAND. 127 

As radius 10.00000 

Is to sin. A, 30° 9.69897 

64 - - - - 1.80618 

40.5 - - - 1.60746 



So is AB, AC 5 



13.11261 



To double the area 1296 perches 3.11261 
4|0)64|8 



4)16 8 

4A. OR. 8P. 

2. What is the area of a triangle, two sides of which 
measure 15.36 chains and 11.46 chains respectively, and 
their included angle 47° 30' ? Ans. 6 A. 1 R. 38 P. 

3. One side of a triangular field bears N. 12° E. dis 
tance 18.23 chains, and at the same station the other ad- 
jacent side bears N. .78° 30' E. distance 13.84 chains: 
required the area. Ans. 11 A. 2R. IIP. 

4. Required the area of a triangular piece of ground, 
one side of which bears N. 82° 30' W. dist. 19.74 chains, 
and at the same station the other adjacent side S. 24° 15 
E. dist. 17.34 chains. Ans. 14 A. 2R. 8 P. 

PROBLEM IV. 

To find the area of a triangle when one side and the tivo 
adjacent angles are given. 

RULE. 

Subtract the sum of the two given angles from 180°; 
the remainder will be the angle opposite the given side. 
Then, 



128 



CONTENT OF LAND. 



[CHAP. 111. 

As the rectangle of radius and the sine of the angle 

opposite the given side, 
Is to the rectangle of the sines of the other angles, 
So is the square of the given side, 
To double the area.* 



EXAMPLES. 



1. In a triangular field ABC, the side AB measures 
76 perches, the angle A 60°, and the angle B 50°: re- 
quired the area. Fig. 47. 



The angle ACB=180° 
and B,=70°. 



the sum of the angles A 



As rad.xsin. C, 
: isin. A X sin. B, 
:: AB 2 =ABxAB, 

: double area in perches 4078 
40)2039 



rad. 


Ar. Co, 0.00000 


sin. C. 70° 


Ar. Co. 0.02701 


sin. A. 60° 


9.93753 


sin. B. 50° 


9.88425 


AB76 


1.88081 


AB76 


1.88081 



4)50 39 



3.61041 



12 A. 2R. 39 P. 



* Demonstration. Let AB, Fig. 49, be the given side of the triangle 
ABC, and A and B the given angles ; also let CD be perpendicular on AB : 
Then by trig. 

sin. ACB : sin. B. : : AB : AC 
rad. : sin. A : : AC : CD. 
Therefore (23.6) rad. X sin. ACB : sin Ax sin. B : : ABx AC : CDx AC : : 
(Cor. 1.6) AB : CD : : AB* : ABx CD ; but ABx CD is equal to double the 
area of the triangle ABC ; therefore (11.5) rad. X sin. ACB : sin. A X sin. B : : 
AB 2 : double the area of the triangle ABC. 



CHAP. III.] 



CONTENT OF LAND. 



129 



2. One side of a triangle measures 24.32 chains, and 
the adjacent angles are 63° and 74° : required the area. 

Am. 37 A. OR. 22 P. 

3. What is the area of a triangular field, one side of 
which is 17.36 chains, and the adjacent angles 37° 30', 



and 48° 15' ? 



Am. 6 A. 3 R. 18 P. 



PROBLEM Y. 

To find the area of a triangle when the three sides are given. 



RULE. 



From half the sum of the three sides subtract each 
side severally ; multiply the half sum and the three re- 
mainders continually together, and the square root of 
the last product will be the area.* 



* Demonstration. Let ABC, Fig. 69, 
be the triangle. Bisect any two of the 
angles, BAC, ABC, by the straight lines 
AG, BG, meeting in G; let fall on the 
three sides of the triangle, the perpen- 
diculars GD, GF, GE, and join GC ; also 
produce AB, AC, and bisect one of the 
exterior angles, HBC, by the line BK, 
meeting AG* produced in K, join KC, 
and let fall the perpendiculars KH, KM, 
and KL. Then (26.1) AD is equal to 
AE and DG to GE ; also BD is equal to 
BF, and DG to GF ; hence GF and GE 
are equal, and consequently (47.1) CF is equal to CE. In like manner it may 
be proved that AH is equal to AL, BH to BM, and CM to CL ; as likewise that 
KH, KM, and KL are equal to each other. Now since BH is equal to BM 
and CL to CM, it is manifest that AH and AL together, are equal to the sum 
of the three sides AB, AC, and BC ; hence AH or AL is equal to the semiperi- 
meter of the triangle ABC. But since twice AD, twice BD, and twice CF are, 
together, equal to the sum of the sides of the triangle, or twice AH, it is ob- 

* The angle BAC is less than the angle HBC (16.1 ;) consequently BAG is less 
than HBK, and BAG, KBA, are together less than HBK, KBA ; but HBK, KBA, 
are together equal to two right angles ; hence BAG, KBA, are less than two right 
angles; therefore (cor. 29.1) the line BK will meet the line AG produced. 

B 




130 CONTENT OF LAND. [CHAP. III. 



EXAMPLES. 



1« Required the area of a triangular tract of land, 
whose three sides are 49.00, 50.25 and 25.69 chains. 



vious that AD, BD and CF together, are equal to AH ; consequently CF is 
equal to BH or BM; hence CM or CL is equal to BF or BD; and therefore 
DH and BC are equal. 

Hence, if from the semiperimeter AH, the three sides AB, AC and BC 
be severally taken, the remainders will be BH, CL, (or BD) and AD re- 
spectively. 

Again, since the angles DBF and DGF are together equal to two right 
angles, as likewise DBF and FBH together equal to two right angles, it is 
manifest that the angle DGF is equal to the angle HBF; and the angle DGB 
to the angle HBK; the triangles DBG and HKB are therefore similar. 
Hence BD : DG : : KH : HB; also in the similar triangles ADG, AHK, AD : 
DG : : AH : HK; therefore (23.6) AD x BD : DG 2 : : AH : HB : : AH* : AH 
XHB. 

If therefore we take between AD and BD, and between AH and HB, the 
mean proportionals M and N respectively, the foregoing analogy will become 
M 2 : DG 2 : : AH 2 : N 2 ; hence (22.6) M : DG : : AH : N ; consequently the 
rectangle M X N is equal to the rectangle AH x DG ; therefore ABC= ABG+ 
BCG+ACG=AHxDG=MxN=V(ADxBD)X V (AHxHB)=v/ (AD 
xBDxHBxAH.) 



IAP. 11I.J 


CONTENT OF 

49.00 
50.25 
25.69 


LAND. 

log. 




Sum 


124.94 




Half sum 
Remainders 


62.47 
C 13.47 
{ 12.22 
( 36.78 

615 chains 


1.79567 
1.12937 
1 08707 
1.56561 




2)5.57772 




2.78886 



131 



61.5 Acres=61 A. 2R. 

2. What is the area of a triangular field whose sides 
measure 10.64, 12.28, and 9.00 chains? 

Ans. 4 A. 2R. 26 P. 

3. What quantity of land is contained in a triangle, 
the sides of which are 20, 30 and 40 chains ? 

Ans. 29 A. OR. 7P 

PROBLEM VL 

To find the area of a trapezium, when one of the diagonals 
and the two perpendiculars, let fall on it from the op- 
posite angles, are given. 



Multiply the sum of the perpendiculars by the diago- 
nal, and half the product will be the area * 



* Demonstration. The area of the triangle ABC (Fig. 70) = 



ACXBF 



ACVDE 
and the area of the triangle ADC= — — ; therefore the sum of- 



132 



CONTENT OF LAND. 



[chap. III. 



Fig. 70. 




Note. — When all the sides and one of the diagonals 
are given, the trapezium will be divided into two trian- 
gles, the area of each of which may be found by the 
last problem. The sum of these areas will be the area 
of the trapezium. 

EXAMPLES. 

1. In a field ABCD, in the 
form of a trapezium, the diago- 
nal AC measures 20.64 chains, 
the perpendicular BF 6.96 chains, 
and DE 5.92 chains ; required the 
area. Fig. 70. 

Ch. 
6.96 
5.92 

12.88 
20.64 

5152 

7728 
2576 

2)265.8432 

132.9216 Ch.=13 A. 1 R, 6 P. 

2. Required the area of a trapezium whose diagonal 
measures 16.10 ch. and the perpendiculars 6.80 ch. and 
3.40 ch. Am. 8 A. OR. 331 P. 

3. The diagonal of a trapezium is 24 ch. and the 
perpendiculars are 8.27 ch., and 12.43 ch. ; what is the 
area? Ana. MA. 3 R. 14 P. 



ACxBF ACxDE BF+DE 

areas, or the area of the trapezium ABCD= , 

XAC. 8 2 a 



CHAP. III.] 



CONTENT OF LAND. 



133 



PROBLEM VII. 

To find the area of a trapezium, when all the angles and 
two opposite sides are given. 

Note. — When three of the angles are given, the fourth may 
be found, by subtracting their sum from 360°. 



RULE. 

Consider one of the given sides and its adjacent an- 
gles, or their supplements when their sum exceeds 180°, 
as the side and adjacent angles of a triangle, and find 
its double area by prob. 4. Proceed in the same man- 
ner with the other given side and its adjacent angles : 
Half the difference of the areas thus found will be the 
area of the trapezium.* 



EXAMPLES. 



Fig. 71. 




1. In a four-sided field ABCD, 
there are given the following 
bearings and distances, viz. AB, 
N. 24° E. dist. 6.90 ch. ; BC, 
N. 64° 40' E. ; CD, S. 35° 20' 
E. dist. 11.50 ch.; and DA, S. 
area. Fig. 71. 

From the given bearings, the angles may be found 
as follows : 



"VY. : required the 



AD, N. 88° E. 
AB, N. 24 E. 

BAD =64° 



CB, S. 64° 40' W. 
CD, S. 35 20 E. 



BCD = 100° 00 



* Demonstration. Let AB, CD, Fig. 71, be the given sides of the tra- 
pezium ABCD. Produce DA, CB, to meet in E ; then 2ABCD == 2EDC— 

2 EDC— 2 EAB 
2E AB or ABCD = ^ . Hence the truth of the rule is evident. 



2 



134 CONTENT OF LAND. [CHAP. III. 

BC, N. 64° 40' E. DC, N. 35° 20' W. 

BA, S. 24 00 W. DA, S. 88 00 W. 



40 40 


123 20 


180 00 


180 00 


=139 20 


ABC=56 40 




Construction. 



Make AB = 6.90, and draw DA, CB, making the 
angle DAB=64°, and ABC=139° 20'; produce DA and 
make the angle EAF = 56° 40'= the given angle ADC; 
lay off AF =11.50= the given side BD, and parallel 
to AD draw FC, meeting BC in C; lastly draw CD 
parallel to AF, meeting AD in D ; then will ABCD be 
the trapezium.* 

Calculation. 

The angle E=180°— the sum of the angles BCD, 
ADC=23° 20'. 



As rad.Xsin. E, 
:sin. EABXsin.EBA, 
: : AB 2 , 



rad. Ar. Co. 0.00000 

sin. E. 23° 20' Ar. Co. 0.40222 
sin. EAB116°00' 9.95366 
sin. EBA 40° 40' 9.81402 
AB 6.90 0.83885 

AB 6.90 0.83885 



2 EAB 70.405 1.84760 



* Demonstration. By construction FC is parallel to AD and CD to AF ; 
therefore (34.1) CD=AF and (29.1) the angle ADC=EAF; hence it is 
evident that the sides AB, CD, and the angles of the trapezium ABCD are 
respectively equal to the given sides and angles. 



CHAP. III.] 



CONTENT OF LAND. 



135 



As radx sin. E, 
sin.ECDxsin. EDC, 
::CD*, 

: 2 EDC 274.731 
2EAB 70.405 



rad. Ar. Co. 0.00000 

sin. E. 23° 20' Ar. Co. 0.40222 
sin. ECD 100° 00' 9.99335 
sin. EDC 56 40 9.92194 
CD 11.50 1.06070 

CD 11.50 1.06070 



2.43891 



2ABCD 204.326 

ABCD= 102.163 Ch.= 10 A. OR. 34.6 P. 

2. In a trapezium ABCD, the angles are, A=65°, B 
=81°, C=120°, and consequently D=94°; also the side 
AB=20 ch. and CD =11 ch. : required the area. 

Ans. 22 A. 2R. 27 P. 

3. Required the area of a four-sided piece of land, 
bounded as follows: 

1. N, 12° 30' E. 

2. N. 81 00 E. dist. 23.20 ch. 

3. S. 36 00 W. 

4.N. 89 00 W. dist. 12.90 ch. 

Ans. 27 A. 2R. 24 P. 

PROBLEM VIII. 

To find the area of a trapezium when three sides and the 
tioo included angles are given. 



As radius, 

Is to the sine of one of the given angles ; 
So is the rectangle of the sides including this 
To a certain quantity. 



136 



CONTENT OF LAND. 



[chap. in. 



As radius, 

Is to the sine of the other given angle ; 

So is the rectangle of the sides including this other 
angle, 

To a second quantity. 
Take the difference between the sum of the given 
angles and 180° ; Then, 

As radius, 

Is to the sine of this difference ; 

So is the rectangle of the opposite given sides, 

To a third quantity. 
If the sum of the angles be less than 180°, subtract 
the third quantity from the sum of the other two, and 
half the difference will be the area of the trapezium. 
But if the sum of the given angles exceed 180°, add 
all the three quantities together, and half the sum will 
be the area.* 




* Demonstration'. Let ABCD (Fig. 
72 or 73) be the trapezium, having the 
given sides, AD, AB, BC, and given 
angles DAB, ABC. Complete the paral- 
lelograms ABCE, ABFD, and join ED, 
CF ; then because EC, DF, are each 
parallel and equal to AB, they are (30.1) 
parallel and equal to each other, and 
(33.1) ECFD is a parallelogram; there- 
fore ABFD = ABHG+GHFD=(35.1) ABCE+ECFD = (34.1) ABCE4- 
2ECD ; to the first and last of these equals add ABCE, then ABFD+ 
ABCE = 2 ABCE+2ECD = 2ABCDE. 

But Fig. 72, when the sum of the given angles DAB, ABC, is less than 
180°, 2ABCDE = 2ABCD+2EAD ; therefore in this case ABFD+ABCE = 
2ABCD + 2EAD; or ABFD + ABCE— 2EAD = 
n Fig. 73. 2ABCD. 

And, Fig. 73, when the sum of the given angles 
DAB, ABC, exceeds 180°, 2ABCDE -2 ABCD— 
2EAD; therefore ABFD+ABCE = 2ABCD— 
2EAD; or, ABFD+ABCE+2EAD = 2ABCD. 

But by prob. 3, one of the first two proportions 
gives 2BAD( = ABFD,) and the other gives S ABC 
(=ABCE;) also because the angle EAD is the 




CHAP. III.] 



CONTENT OF LAND. 



137 



EXAMPLES. 



1 In a trapezium ABCD, there are given AD= 23.32 
ch., AB=25.70 ch., and BC= 15.84 ch., the angle DAB= 
64°, and ABC=82°: required the area. 



As rad. 

: sin. DAB, 64° - - - - 
. : AD X AB,j AD 23.32 


Ar. Co 

Ar. Co. 


. 0.00000 
9.95366 
1.36773 
1.40993 


: first quantity 538.66 

As rad. 

: sin. ABC, 82° - - - - 

.. ABvRr 5 AB 25.70 
:.ABxBC, ^ BC1584 


2.73132 

, 0.00000 
9.99575 
1.40993 
1.19975 



second quantity 403.12 



2.60543 





DAB 


64° 




ABC 


82 

146 

180 




Difference 


34° 


As rad. 


_ 


. 


: sin. difference 34° 


. 



::AD X BC, j 

: third quantity 206.55 



Ar. Co. 0.00000 

- - 9.74756 

AD 23.32- - 1.36773 

BC 15.84- - 1.19975 



2.31504 



difference between the sum of the given angles and 180°, and the side 
EA=BC, the third proportion gives 2 EAD : hence the truth of the rule 
is manifest. 

12* S 



138 CONTENT OF LAND. [CHAP. III. 

1st quantity 538.66 
2d " 403.12 



941.78 
3d " 206.55 



2)735.23 

367.615 ch. = 36 A. 3 R. 2 P. 

2. What is the area of a four-sided lot of ground, 
three sides of which, taken in order, measure 6.15, 8.46, 
and 7.00 chains, respectively ; the angle contained by 
the first and second sides 56°, and that contained by the 
second and third sides 98° 30'? 

i? w .4A.0R. 25 P. 

3. One side of a quadrilateral piece of land bears S. 
Ih E. dist. 17.53 ch., the second, N. 87 E. dist. 10.80 
ch. and the third, N. 251 E. dist. 12.92 ch. : what is 
the area? Arw. 21 A. 3 R. 2 P. 

PROBLEM IX. 

To find the area of a trapezoid. 

RULE. 

Multiply the sum of the parallel sides by their per- 
pendicular distance, and half the product will be the 
area.* 

EXAMPLES. 

1. Required the area of a trapezoid ABCD, of which 
the parallel sides AD, BC measure 6.14 and 9.48 chains, 

Fig. 74. * Demonstration. The trapezoid ABCD, Fig. 

74, = the triangle ABD + BDC = (by prob. 2,) 

■ (because BF=DE,) AD * BF 




CHAP. III.] CONTENT OF LAND. 139 

respectively, and their perpendicular distance BF or DE, 
7.80 chains. 

Ch. 

6.14 

9.48 



15.62 

7.80 

124960 
10934 

2)121.8360 

60.9180 Ch.= 6 A. R: 15 P. 

2. The parallel sides of a trapezoid are 12.41 and 8.22 
chains, and their perpendicular distance 5.15 chains : 
required the area. Ans. 5 A. 1 R. 10 P. 

3. Required the area of a trapezoid whose parallel 
sides are 11.34 and 18.46 chains, and their perpendicular 
distance 13.25 chains. Ans. 19 A. 2 R. 39 P. 

PROBLEM X. 

To find the area of a circle, or of an ellipsis.^ 

RULE. 

Multiply the square of the circle's diameter, or the 



* If two pins be set upright in a plane, and a thread, the length of 
which is greater than twice the distance between the pins, having the 
ends tied together, be put about the pins ; and if the point of a pin or 
pencil applied to the thread, and held so as to keep it uniformly tense, be 
moved round, till it return to the place from which the motion began ; then 
the point of the pin or pencil will have described on the plane, a curved 
line called an Ellipsis. 



140 CONTENT OF LAND. [CHAP. III. 

product of the two diameters of the ellipsis, by .7854, 
for the area * 

Note 1. — If the diameter of a circle be multiplied by 
3.1416, the product will be the circumference; also if 
the circumference be divided by 3.1416, the quotient 
will be the diameter. 

2. If the area of a circle be divided by .7854, the square 
root of the quotient will be the diameter. 

EXAMPLES. 

1. How many acres are in a circle a mile in diameter? 
1 mile=80 ch. 
80 



6400 
.7854 


[. Ch.=502 A. 2 I 

by Logarithms. 
f 80 
1 80 

.7854 




3141600 
47124 




5026.5600 Sc 
Or 
Square of 80 


I. 25 P. nearly. 

log. 1.90809 
1.90309 

—1.89509 



5026.56 Sq. Ch. 3.70127 

. Required the area of an ellipsis, the longer diameter 



of which measures 5.36 ch. and the shorter 3.28 ch. 



* The demonstration of this rule is too abstruse to admit of a place in 
this work. The student who wishes to see a demonstration is referred to 
a treatise on Mensuration or Fluxions. 



CHAP, in.] CONTENT OF LAND. 141 

Ch. 

5.36 

. 3.28 



4288 
1072 
1608 

17.5808 

.7854 

703232 
879040 
1406464 
1230656 

13.80796032 Sq. Ch.= l A. 1 R. 20.9 P. 

PROBLEM XI. 

The bearings and distances of the sides of a tract of land 
being given, to calculate the area, 

RULE. 

1. Rule a table and head it as in the annexed example ; 
observing that the letters E. D. D. and W. D. D., stand 
for East Double Departure and West Double Departure. 

2. Find by prob. 12. chap. 1., the corrected differ- 
ences of latitude and the departures, corresponding to 
the several sides, placing them in their proper places in 
the table. 

3. When the departures corresponding to the first and 
last sides are of the same name, add them together, and 
place the sum opposite the first side, in the column of 
double departures, which is of that name ; but when they 
are of different names, take their difference, and place it 



142 CONTENT OF LAND. [CHAP. III. 

in the column ot double departures, which is of the same 
name with the greater departure. Proceed in the same 
manner with the departures corresponding to the first 
and second sides, placing the result opposite the second 
side ; with those corresponding to the second and third 
sides, placing the result opposite the third side ; and so 
on to the last. 

4. Commencing with any side of the survey at plea- 
sure, assume any number whatever for a multiplier cor- 
responding to that side, and place it in the column of 
multipliers, opposite to the side, marking it with the let- 
ter E, for east. If this multiplier and the double depar- 
ture, corresponding to the next side, are of the same name, 
take their sum for the next multiplier, marking it with 
tliat name ; but if they are of different names, take their 
difference, marking it with the name of the greater. 
Proceed in the same way with this multiplier and the 
next double departure ; and so on till multipliers have 
been found corresponding to all the sides. 

5. Multiply each of the corrected differences of lati- 
tude by its corresponding multiplier ; and when the mul- 
tiplier is east, place the product in that column of areas, 
which is of the same name with the difference of latitude ; 
but when it is west, place the product in the column of 
areas, which is of a different name from that of the dif- 
ference of latitude. 

6. Add up the numbers in the columns of areas, and 
taking the difference of their sums, divide it by 2 ; the 
result will be the area of the survey.* 



* Demonstration. Let ABCDEFG, Fig. 79, be a plot of a survey ; and 
let the east and west line AL, represent the assumed multiplier. From the 
points B and L draw BM parallel, and LM perpendicular to AL, meeting in 



CHAP. III.] CONTENT OF LAND. 143 

JSote 1. — If the double departures have been correctly 
found, the sums of the numbers in the two columns, \vjl] 
be equal. Also, if the multipliers have been correctly ob- 
tained, the sum or difference of the multiplier last found 




M ; and bisect BM by tbe meridian NS. Draw the other east and west 
lines, Cc, md, ne, rf, and ug ; and also the meridians hk, Bp, Cn, Ds, ur, 
Fw, and Gx. Then it is evident that the differences of latitude and the de- 
partures corresponding to the several sides will be as in the following' table. 
Also according to the rule, Bh-\- Av=Bx, is the double departure correspond- 
ing to the first side ; Bh-\- Cl=Ck, is that for the second side; CI — Dm=Dp, 
is that for the third ; and so on to the last. 



Dist. 


N. 


S. 


E. 


W. 


E.D.D. 


W.D.D 


Multipliers. |N. Areas. 


S. Areas. 


AB 
BC 


Ah 




Bh 




Bx 




Aa+Bb, E 


2Aab B 




Bl 


CI 




Ck 




Bb+Cc,E 




2 BbcC 


CD 




Cm 




Dm 


Dp 




Cc+Dd, E 




2 CcdD 


DE 
EF 
FG 
GA 


Ft 

Gv 


Dq 

Er 


Eq 

Av 


Fr 
Gt 




En 


Dd+Ee,E 




2 DdeE 




Fs 


Ee+Ff, E 




2 Ee/F 




Gu 


Ff+Gg,E 


2FfgG 




Aid 




Gg+Aa,E 


2Gga A 





144 



CONTENT OF LAND. 



[CHAP. III. 



and the next double departure, according as they arc of 
the same or different names, will be equal to the assumed 
multiplier. 

2. It is best in general, to assume 0, for the first mul- 
tiplier ; as by so doing there is one multiplication less 
to be performed, and the other multipliers are mostly 
smaller numbers, than they would otherwise be. 



By construction, the assumed multiplier AL=Aa-|-aL=Aa-}-&M=A<T 
+B6. By proceeding with this multiplier and the double departures, as 
directed in the rule, we shall evidently have the other multipliers as re- 
presented in the table. It is also plain that the products of the differences 
of latitude by these multipliers, will be as represented in the columns of 
north and south areas. 

The sum of the north areas is 2 BAGF/6B ; and the sum of the south 
areas is 2 BCDEF/6B. The difference of these is 2 ABCDEFGA ; the 
half of which is the area of the survey. 

The preceding demonstration may easily be extended to the case in which 
the assumed multiplier is so small as to make the meridian NS pass through 
the survey. Thus, suppose Aw+HB to be the assumed multiplier, the 
meridian in this case coinciding with FH. Then the multipliers will be 
equal to the differences between the above multipliers and the quantity, 
iva+bll or its equal 2&H. We may therefore represent them, and the 
products, as in the following table ; in which the multipliers are marked, 
and the products placed, in conformity with the rule. 



Dist. 


N. S. 


Multipliers. 


N. Areas. 


S. Areas. 


AB 
BC 


Ah 

\Bl 

\ 


(Aa+ Bb)—2 bH, E. 


2 AnBb—2wabH 




(Bb+Cc)—2bH, E. 




2 BbcC—2HbcK 


CD 




Cm 


(Cc+Dd)— 2 6//E. 




2 CcdD—2KcdP 


DE 




Dq\(Dd+Ec)—2bH,E. 




2 DJcE~2PdeQ 


EF 




Er\(Ec+Ff)—2bH,E. 




2 EefF—2 Qe/F 


FG 


Ft 


2 bH—(Ff+ Gg) W. 




2Ffgt~2FfgG 


GA 


Gv 


\2bH—(Gff+Aa) W. 




2 tgaw—2 GgaA\ 



CHAP, m.] CONTENT OF LAND. 145 

3. Instead of assuming the first multiplier east, it 
might with equal propriety be assumed west. Also 
instead of finding the multipliers from the departures, 
they might be found in a similar manner, from the differ- 
ences of latitude ; using, in that case, the departures for 
multiplicands. 

4. When one or two bearings or distances are omitted, 
they may be found by the problems in the last chapter; 
and in these cases the differences of latitude and depar- 
tures are to be used as first obtained from the tables, 
there being no means of correcting them. 

EXAMPLES. 

1. Given the bearings and distances of the sides of a 
tract of land as follows : 1st. 401° E. 31.80 ch.; 2d. N. 
54° E. 2.08 ch.; 3d. N. 291° E. 2.21 ch.; 4th. N. 28f° E. 
35.35 ch.; 5th. N. 57° W. 21.10 ch.; and 6th S. 47° W. 
31.30 ch. ; to the place of beginning. Required the area 
of the tract. 



The sum of the north areas is 2 AabB — 2 Hbaw : and the sum o r the south 
areas is 2 BCDEF/6B+2 wafF — 2 RbfF— 2 AGF/a=2 BCDEF/6B+ 
2 wafF—2 waf F— 2 Bbaw — 2 AGF>=2 BCDEF/5B-2H5at«-2AGF/o 
=2BCDEF/6B — 2 AGF/a— 2 Ubaw. If now the sum of the north areas be 
subtracted from that of the south areas, the remainder will be 2 BCDEF/&B 
—2 AGFfa—2 Aa6B=2 BCDEF/6B-2 BAGF/6=2 ABCDEFGA. 



13 



146 



CONTENT OF LAND. 



[chap, hi. 



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2. Required the area of a tract of land, bounded as 
follows: 1st. N. 75° E. 13.70 ch. ; 2d. N. 20i° E. 10.30 
ch,; 3d. East, 16.20 ch. ; 4th. S. 33*° W. 35.30 ch. ; 
5th. S 76° W. 16 ch.; 6th. North, 9ch.; 7th. S. 84° 



CHAP III.] CONTENT OF LAND. 147 

W. 11.60 ch. ; 8th. N. 53* ° W. 11.60 ch. ; 9th. N. 36| 
E. 19.36 ch.; 10th. N. 22i° E. 14 ch.; 11th. S. 761° E. 
12 ch. ; 12th. S. 15° W. 10.85 ch. ; 13th. S. 18° W. 10.62 
ch. ; to the place of beginning. 



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148 CONTENT OF LAND. [CHAP. III. 

3. Given the boundaries of a tract of land as follow, 
viz. lst.S.35i° W. 11.20 ch.; 2d. N. 45° W. 24.36ch.-; 
3d. N. I5F E. 10.80 ch. ; 4th. S. 77° E. 16. ch. ; 5th. N. 
87|° E. 21.50 ch. ; 6th. S. 60° E. 14.80 ch. ; South 10.91 
ch.; 8th. N. 85° W. 29.28 ch. ; to the place of beginning : 
required the area. Ans. 85 A. 3 R. 17 P. 

4. Given the boundaries of a tract of land as follow, 
viz. 1st. N. 19° E. 27 ch. ; 2d. S. 77° E. 22.75 ch. ; 3d. 
S. 27° E. 28.75 ch.; 4th. S. 52° W. 14.50 ch. ; 5th. S. 15f 
E. 19 ch.; 6th. West, 17.72 ch. ; 7th. N. 36° W. 1 1.75 ch. ; 
8th. North, 16.07 ch. ; 9th. N. 62° W. 14.88 ch. ; to the 
place of beginning : required the area. 

Ans. 152 A. 2R. 6 P. 

5. Required the area of a tract of land bounded as 
follows : 1st. S. 62° W. 7.57 ch. ; 2d. N. 43£° W. 5.89 ch. ; 
3d North, 5.82 ch. ; 4th. N. 33i° W. 8.83 ch. ; 5th. N. 48° 
E. 4.81 ch. ; 6th. N. 12° E. 4.66 ch. ; 7th. N. 62i° E. 5.27 
ch.; 8th. S.6FE. 5.60 ch.; 9th. S.40£°E. 5.87 ch. ; 10th. 
East, 6.54 ch. ; 11th. North, 5.52 ch. ; 12th. N. 68i° E. 
3.10 ch. ; 13th. S. 30° E. 7.90 ch. ; 14th. S. 23° W. 8.80 
ch.; 15th. S.31FE. 6.42 ch.; 16th. S. 50° W. 8.40 ch. ; 
17th. N. 44° W. 6.85 ch. to the place of beginning. 

Ans. 44 A. 2R. 22 P. 

6. Given the following field-notes to find the area of 
the survey ; also the bearings and distance of the 3d side, 
which were omitted to be taken on account of obstacles 
in the way. 

Ch. 

1. S. 85i° E. 23.30 

2. S. 19 E. 31.12 

3. 

4.N.64 W. 29.72 



chap, in.] 



CONTEXT OF LAND. 



149 







Ch. 


5. 


N. 154° 


W. 22.46 


6. 


N. 58 


E. 25.94 


7. 


S. 271 


E. 6.60 



Ans. Area 182 A. OR. 21.7 P. and the bearing and 
distance of the 3d side, S. 66° 23' W. 28.06 ch. 

7. Being furnished with the field-notes of a tract of 
land, and requested to calculate the area, I found on 
examining them, that the figures expressing the angles 
of bearing of the 4 th and 5 th sides were so defaced as 
to be illegible : but as the remaining data are sufficient, 
the area is required. The field-notes are as follows : 

Ch. 

1. S. 601° W. 10.34 

2. N. 27i W. 17.88 

3. N. 51 E. 15.85 
4.N. — E. 9.61 

5. S. — E. 19.18 

6. SL 161 E. 22.21 

7. S. 71i W. 16.66 
8.N. 7H W. 5.76 

Am. 81 A. 2 R. 23 P. 

8. In a survey, represented 
Fig. 81, the corner at A was 
inaccessible, occasioned by the 
overflowing of water ; but being 
a tree, it can be seen from the 
adjacent corners B and L. I 
therefore set my instrument at 
B and took the bearing to A, 
which I reversed, and set in 
my field-book as the first bear- 
ing. I then proceeded to take 
the bearings and distances of 
the several sides to L ; and at 
L, I took the bearing of the 
side LA. The field-notes being as follows, the length 
of the sides AB and LA, and the area are required. 

13* 




150 



CONTENT OF LAND. 



[CHAP. III. 





1 


Fig 
I 

•2 


80 - AB,N.51J°W. Ch. 
BC, S.45i W. 15.16 




1 




^^^3 CD, N. 50 W. 22.10 
i/T DE, North, 18.83 

* MnJI EF ' N - 48 K 22 - 60 












/if/ fc FG,N.25£ W. 20.17 
\ 3)\ W GH,East, 26.57 

J %hJm m > s - 3(H E - 22 - 86 


5! . 






\ W*fir ik ; S.44 W. 15.04 

. \| KL,S.47 E. 28.55 

LA,S.20^ W. 




[ iws.AB, 26.47 ch.; 
LA, 23.81 ch. ; and the area 244 A. 3 R 13 P. 



9. In taking a survey of a tract of land bounded by 
six straight sides, Fig. 80, 1 was prevented going directly 
from the 3d to the 4th corner by a pond of water. I 
therefore set up two stakes near the edge of the pond, 
and took the bearing and distance from the 3d corner 
to the first stake, from the first stake to the second, and 
from the second to the 4th corner, and noted them in 
my field-book as all belonging to the 3d station of the 
survey. The field-notes being as follows, the bearing 
and distance of the 3d side, and the area of the survey 
are required. 

1. North, 7.81 Ch. 

2. S. 76i° E. 18.15 



W. 10.70) 

. 13.92 y 



(S. 52 
MS. 7* 

I S. 33i 

4. N. 84* 

5. N. 4i 

6. East. 
Ans. 3d side, S. 10° 47' W. 28.42 ch. 

80 A. R. 25 P. 



W. 1D.VZ 

E. 9.00 J 

W. 27.12 

W. 22.00 

16.58 



and area 



CHAP. III.] CONTENT OF LAND. 151 

PROBLEM XII. 

To find the area, when off-sets are taken. 

RULE. 

1. Find by the last problem, the area enclosed by the 
stationary lines and straight sides of the survey. 

2. Subtract the stationary distance of each off-set, 
from that of the one immediately following; the remain- 
ders will be the distances, intercepted on the stationary 
line, between each two adjacent off-sets. Place these 
under one another in a column as in the annexed exam- 
ples. Also take the sums of each two adjacent off-sets, 
and place them in the next column, so as to correspond 
with the intercepted distances. 

3. Multiply the sum of each two adjacent off-sets by 
their intercepted distance on the stationary line ; then, 
half the sum of the products will be the area of the off- 
sets on that line. 

4. If there are off-sets on more than one stationary 
line, proceed in the same manner with the others. 

5. When the stationary lines are within the boundary 
of the survey, add the areas of the off-sets to the area 
enclosed by the stationary lines and straight sides ; but 
when the stationary lines are without the boundary, sub- 
tract the areas of the off-sets.* 



* Demonstration. Considering the boundary as straight between the 
ends of each two adjacent off-sets, it is plain that the area contained between 
the stationary line and boundary will be divided by the off-sets into trape- 
zoides and triangles. Hence the truth of the rule is evident 



152 



CONTENT OF LAND. 



[CHAP. 



III. 



EXAMPLE 1, Fig. 82. 



Required the area of a piece of meadow, bounded on 
one side by a brook ; the field-notes being as follows : 



Left-hand off-sets on the stnt line. 



1. N. 16i°E. 14.35 Ch 

2. East, 7.82 

3. S. 3iW. 14.45 Stat, line 

4. N. 86 J W. 11.07 

Fig. 82. 



Stat. 

No. 1. 



2. 




Dist. 

0.00 Ch. 

0.95 

2.03 

3.28 

5.20 

7.43 

8.98 
10.46 
11.71 



10. 14.45 



Off-sets. 

0.30 Ch. 

0.84 

0.86 

0.50 

1.80 

2.35 

1.45 

1.08 

1.85 

0.35 



The area of the part 
ABCD will be found, 
by the last problem, to 
be 13 A. 1 R. 11 P. 




CHAP. III.] CONTENT OF LANI>. 



153 



To find the area of the off-sets. 



No. 


Sta. Dist. 
Ch. 


Off-sets. 

Ch. 


Intercep. 
Dist. 


Sums of 
Off-sets. 


Products. 


1 


0.00 


0.30 








2 


0.95 


0.84 


0.95 


1.14 


1.0830 


3 


2.03 


0.86 


1.08 


1.70 


1.8360 


4 


3.28 


0.50 


1.25 


1.36 


1.7000 


5 


5.20 


1.80 


1.92 


2.30 


4.4160 


6 


7.43 


2.35 


2.23 


4.15 


9.2545 


7 


8.98 


1.45 


1.55 


3.80 


5.8900 


8 


10.46 


1.08 


1.48 


2.53 


3.7444 


9 


11.71 


1.85 


1.25 


2.93 


3.6625 


10 


14.45 


0.35 


2.74 


2.20 


6.0280 




2) 


37.6144 



18.8072 Ch. 
=1 A. 3R. 21 P. 



A. R. P. 
AreaofABCD 13 1 11 
Do. of off-sets 1 3 21 



Whole area 15 32 

Example 2. Fig. 83. 

Required the area of a survey from the following field 
notes. U 



154 



CONTENT OF LAND. 



[CHAP. III. 



Left hand off-sets. 
1st. Stationary Line. 3d Stat Line. 
Sta. Dist. Off-sets. Sta. Dist. Off-sets. 







Ch. 




No. 


Ch. Ch. 


No. Ch. Ch. 


1. N. 36f ° 


W. 


30.00 




1. 


0.00 0.50 


1. 0.00 0.55 


2. N. 56£ 


E. 


21.60 stat. line. 


2. 


6.10 3.40 


2. 4.20 2.50 


3. N. 26£ 


E. 


13.44 


Do. 


3. 


10.15 3.10 


3. 8.05 3.20 


4. S. 71£ 


E. 


18.96 


Do. 


4. 


14.08 3.96 


4. 15.15 2.45 


5. S. 26| 


E. 


13.46 


Do. 


5. 


19.20 2.70 


5. 18.96 0.50 


6. S. 45 


W. 


42.41 




6. 
2d. 
1. 
2. 


21.60 0.55 
Stat. Line. 
0.00 0.55 
13.44 0.55 


4th Stat. Line. 

1. ().()() 0.50 

2. 5.12 2.75 

3. 10.00 1.90 

4. 13.46 0.70 



The area within the stationary lines and straight sides, 
found by the last problem, is 1152.5381 square chains. 

To find the area of the off-sets. 

1st. Stationary Line. 



No. 


Sta. Dist. 
Ch. 


Off-sets. 
Ch. 


Intercep. 
Dist. 


Sums of 
Off-sets. 


Products. 


1 


0.00 


0.50 








2 


6.10 


3.40 


6.10 


3.90 1 23.7900 


3 


10.15 


3.10 


4.05 


6.50 


26.3250 


4 


14.08 


3.96 


3.93 


7.06 


27.7458 


5 


19.20 


2.70 


5.12 


6.66 


34.0992 


6 


21.60 


0.55 


2.40 


3.25 


7.8000 



2d. Stationary Line. 



No. 


Sta. Dist 
Ch. 


Off-sets. 
Ch. 


Intercep. 
Dist. 


Sums of 
Offsets. 


Products. 


1 


0.00 


0.55 








2 


13.44 


0.55 


13.44 


1.10 


14,7840 



CHAP. III.] 



CONTENT OF LAND. 

3d. Stationary Line. 



155 



No. 


Sta. Dist. 
Ch. 


Off-sets. 
Ch. 


Intercep. 
Dist. 


Sums of 
Off-sets. 


Products. 


1 


0.00 
4.20 


0.55 








2 


2.50 


4.20 


3.05 


12.8100 


3 


8.05 


3.20 


3.85 


5.70 


21.9450 


4 


15.15 


2.45 


7.10 


5.65 


40.1150 


5 


18.96 


0.50 


3.81 


2.95 


11.2395 



4th. Stationary line. 



1 


0.00 


0.50 








2 


5.12 


2.75 


5.12 


3.25 


16.6400 


3 


10.00 


1.90 


4.88 


4.65 


22.6920 


4 


13.46 


0.70 


3.46 


2.60 


8.9960 



2)268.9815 



Area of the off-sets - - - 
Area within the stationary lines 



134.49075 Ch. 
1152.5381 



1287.02885 Ch. 

128.702885 Acr 
4 



2.811540 
40 

32.46160 



Area of the survey, 128 A. 2 R. 32 P. 



156 CONTENT OF LAND. [CHAP. ffl. 



EXAMPLE 3. 

Required the area of a meadow from the following 
field-notes. 

Left-hand off-sets on the stat, line. 
Sta. Dist Off-sets. 

l.N.41i°E. 14.35 Ch. No. 1. 0.00 Ch. 0.38 Ch. 
2. S.42i E. 14.71 Sta. line. 2. 2.65 2.35 



3. S. 54 W. 16.32 


O. 


3.80 


1.70 


4.N.32* W. 11.50 


4. 


6.00 


2.75 




5. 


7.50 


1.40 




6. 


9.60 


3.20 



7. 12.38 2.72 

8. 14.71 0.42 
j4rcs.Area22A. 3 R. 27 P. 



EXAMPLE 4. 

The following field notes are given, to find the area 
of the survey. 

Left-hand off-seta. 
On the 1st stat. line. On the 2d stat. line 

Sta. Dist. Offsets. Sta. Dist. Off-seta 



Ch. 




No. 


. Ch. Ch. No.Ch. Ch. 


1. S.69i°E. 16.14 sta. line 1. 


0.00 0.44 1. 0.00 0.31 


2. S.28 E. 9.38 


Do. 


2. 


3.80 2.00 2. 2.67 2.94 


3. S. 321 W. 21.20 




3. 


7.04 3.79 3. 6.20 2.62 


4.N.48 W. 22.47 




4. 


9.87 2.34 4. 9.38 0.39 


5.N.26I E. 19.00 




5. 


13.24 3.00 






6. 


16.14 0.31 



Ana. 56 A. 2 R. 18 P. 

PROBLEM XIII. 

Given the hearing and distance of two stations from each 
other and the hearings of cdl the corners of a tract of 
land from these statio?is, to find the area of the tract. 

The method of doing this will be best explained by 
an example. 



CHAP. HI.] 



CONTENT OF LAND. 



157 



EXAMPLE 1. 

Let ABCDEFGA, Fig. 84, represent a field, all the 
angles of which can be seen from two stations, H and 
I, without it. The bearing and distance of the stations, 
and the bearings of all the angles of the field, from each 
station, being as follow, it is required to find the area. 

Fig. 84. d 




The station H bears from the station I, North, dist. 
28. Ch. 





Bearings. 




Bearings. 


HA 


S. 81i°E. 


IA 


N.28i°E. 


HB 


S. 851 E. 


IB 


N.42£ E. 


HC 


S. 68 E. 


IC 


N.51J E. 


HD 


S. 58i E. 


ID 


N. 71 E. 


HE 


S. 35J E. 


IE 


S. 82 \ E. 


HF 


S. 28J E. 


IF 


N. 731 E. 


HG 


S. 40 E. 


IG 


N. 60 E. 



Construction. 
Draw HI according to the given bearing and distance ; 

and from the points H and I, draw HA, HB, HC, &c, 
14 



158 CONTENT OF LAND. [CHAP 111. 

and IA, IB, IC, &c. according to the given bearings; 
then will the intersections A, B, C, &c. of the corres- 
ponding bearings HA and IA, HB and IB, HC and IC, 

&c. be the angular points of the field. 

Calculation. 

In each of the triangles IHA, IHB, IHC, &c. we have 
the side IH ; and from the bearings of the sides, we have 
all the angles, to find the sides IA, IB, IC, &c. 

Then in each of the triangles, IAB, IBC, ICD, &c. we 
have two sides, and the included angle ; whence the areas 
may be found by prob. III. 

From the sum of the areas of the triangles IAB, IBC, 
ICD, and IDE, which is equal to the area IABCDEI, 
subtract the sum of the areas of the triangles IAG, IGF 
and IFE, which is equal to the area IAGFEI ; the re- 
mainder will be the area of the field ABCDEFGA. 

Note. — In working the proportions for finding the sides 
IA, IB, &c. it will be unnecessary, when the area only 
is required, to take out the natural numbers correspond- 
ing to the logarithms of those sides ; because in the pro- 
portion? for finding the areas it will be sufficient to know 
the logarithms of the sides, without knowing their real 
lengths. 

To find the log. of IA. 

As sin. HAI, 70° 00' 9.97299 

: sin. AHI, 81 30 9.99520 

: : IH, 28 1.44716 

11.44236 

: IA, log. 1.46937 



CHAP. III. J CONTENT OF LAND. 159 

To find the log. of IB. 

As sin. HBI 52° 00' 9.89653 

: sin. BHI85 45 9.99880 

: : IH 28 1.44716 



11.44596 



: IB log. 1.54943 

To find the log. of IC. 

As sin. HC1 60° 30' 9.93970 

: sin. CHI 68 00 9.96717 

: : IH 28 1.44716 



11.41433 



: IC log. 1.47463 

To find the log. of ID. 

As sin. HDI 50° 45' ----- 9.88896 

: sin. DHI58 15 9.92960 

: : IH 28 1.44716 



11.37676 
: ID log. 1.48780 



o 



To find the log. of 'IE. 

As sin. HEI 47° 00' 9.86413 

: sin. EHI35 30 9.76395 

: : IH 28 1.44716 



11.21111 



IE log. 1.34698 



160 CONTENT OF LAND. [CHAP. III. 

To find the log. of W. 

As sin. HF1 78° 00' 9.99040 

: sin. FHI28 30 9.67866 

: : IH 28 - 1.44716 

11.12582 

: IF log. 1.13542 

To find the log. of \G<. 

As sin. HGI 80° 00' 9.99335 

: sin. GHI40 00 - 9.80807 

: : IH 28 1.44716 

11.25523 

: IG log. 1.26188 

To find the double area of the triangle I AB. 

Asrad. 10.00000 

: sin. AIB 13° 45' 9.37600 

• LWIB $ IA lo §- L46937 

•' 1AX1B '(IB 1.54943 

: 2IAB 248.2 2.39480 

To find the double area of the triangle IBC. 

As rad. 10.00000 

: sin. BIC 9° 15' 9.20613 

.. IB vIC \ lB lo £- L54943 

..ItfX-K,, J IC 1.47463 

: 2IBC 169.9 2.20319 



CHAP. III.] CONTENT OF 1.AND. 161 

To find the double area of the triangle ICD. 

As rad. 10.00000 

: sin. CID 19° 30' 9.52350 

.TCxID J IC ■ lo S' 1 ' 47463 

..lUXli^ ID 1.48780 

: 2ICD, 306.15 2.48593 

To find the double area of the triangle IDE. 

As rad. 10.00000 

: sin. DIE 26° 30' 9.64953 

- -IDxIE $ ID l0 S- lA8780 

. .iuxii% £ IE 1.34698 

: 2IDE 305.007 2.48431 

To find the double area of the triangle IEF. 

As rad. 10.00000 

sin. EIF 24° 00' 9.60931 

• IFvTF J IE l0 S* 1 * 34698 

• -"-XUSjiF 1.13542 

: 2IEF 123.511 ------ 2.09171 

To find the double area of the triangle IFG. 

As rad 10.00000 

: sin. FIG 13° 30* 9.36818 



ifxig,^ : 



log. 1.13542 
1.26188 



2IFG 58.274 1.76548 

14* X 



162 



CONTENT OF LAND. 



[CHAP. III. 



To find the double area of the triangle I AG. 

Asrad. 10.00000 

: sin. AIG 31° 30' 9.71809 

•IAXIG ! IA log. 1.46937 

..IAXIG, | IG 1261g8 

: 2IAG 281.412 2.44934 



2IAB - - - 

2IBC - - - 

2ICD - - - 

2IDE - - - 

2IABCDEI 
2IAGFEI 

2ABCDEFGA 
ABCDEFGA 



2IEF 
2IFG 
2IAG 



2 IAGFEI 



Ch. 

248.2 
169.9 
306.15 
305.007 

1029.257 
463.197 

566.060 



283.03 Ch. =21 A. IE. 8 P. 



Ch. 

123.511 

58.274 
281.412 

463.197 



The bearings and distances of the sides, if required, 
might readily be obtained. For, having found the 
distances IA, IB, we have in the triangle IAB, two 
sides, and an included angle; whence the angle IAB 
and side AB may be found. The angle IAB applied 
to the bearing of IA, will give the bearing of AB. In 
the same manner the bearings and distances of the 
other sides may be found. 



example 2. 

Being required to calculate the area of a field, the 
owner of which refuses permission to go on it, I choose 
two stations, F and G, in the adjacent land, from whence 



CONTENT OF LAND. 



163 



CHAP. III.] 

•ill the angles of the field are visible. The bearing and 
distance of the stations, and the bearings of the angles, 
from each station, are as follow. What is the area of 
the field ? 

The station G bears from the station F, N. 43° W. 
20 ch. 





Bearings. 




Bearings. 


FA 


N 25£° E. 


GA 


S. 66° E. 


FB 


N. 19 W. 


GB 


N. 23 E. 


FC 


N. 5 W. 


GC 


N.38£E. 


FD 


N. 16 E. 


GD 


N.60£E. 


FE 


N. 60i E. 


GE 


S. 84 E. 



Arts. 33 A. 1 R. 7 P. 



PROBLEM XIV. 

Tojlnd the area of a survey by protracting it, and dividing 
the plot into triangles and trapeziums. 

The method of doing this will be easily understood 
from the following example. 

Example 1. 

Given the bearings and distances of the sides of a 
tract of land as follow: 1st. N. 50° E. 9.60 ch. ; 2d. S. 
32° E. 16.38 ch.; 3d. S. 41° W. 6.30 ch. ; 4th. West, 
8.43 eh. ; 5th. N. 79° W. 10.92 ch. ; 6th. N. 5° E. 11.25 
ch. ; 7th. S. 83° E. 6.48 ch. ; to the place of beginning. 
Required the area. 

Fig. 75, is a plot of this survey : and by drawing the 
lines as in the plot, it is divided into two trapeziums 
AGFE, AEDF, and a triangle BDC. Measure the 



164 CONTENT OF LAND. [CHAP. III. 

several bases and perpendiculars, on the same scale that 
was used in the protraction, and find the double areas of 
the triangle and trapeziums by probs. 2 and 6 ; the sum 
of these will be the double area of the survey. 



Perpens. 

EG 16.68 x | ^ 4 ^ ] =203.6628=2 AGFE 

EB 19.17 x | j^g 10 ( = 267 - 4215 = 2 AEDB 
BD 19.23 x Ce5.16 = 99.2268=2 BDC 

2)570.3111 ch.=2 ABCDEFG 

285.15555 ch.=28A. 2R. 2P. 
= the area required. 

Example 2. 

The following field-notes are given to protract the 
survey and find the area. 







Ch. 






1. N. 15° 


00' E. 


20 






2. N. 37° 


30' E. 


10 






3. East 




7.50 






4. S. 11° 


00' E. 


12.50 






5. South 




13.50 






6. West 




10. 






7. S. 36° 


30' W. 10. 






8. N. 38° 


15' W 


. 8.50 










Ans. 46 A. 


2R. 


9P 



CHAPTER IV. 



LAYING OUT AND DIVIDING LAND. 

PROBLEM I. 

To lay out a given quantity of land in a square form. 

RULE. 

Reduce the given quantity to chains or perches, and 
extract the square root, which will be the length of a 
side, of the same denomination to which the given quan- 
tity is reduced. 

EXAMPLES. 

1. Required the side of a square that shall contain 
9A. 3R. 28P. 

40)28 Per. 

4)3.7R. 

9.925 A.=99.25 ch. 

Ch. 
99.25(9.96 ch. the length of a side. 
81 



189)1825 
1701 



1986)12400 
11916 



484 

165 



16G LAVING OUT AND DIVIDING LAND. [CHAP. IV. 

2. Required the side of a square tract of land that 
shall contain 325 acres. Ans. 57 chains. 



PROBLEM II. 

To lay out a given quantity of land in a rectangular form, 
having one side given. 

RULE. 

Divide the given content by the length of the given 
side, the quotient will be the length of the required side. 

EXAMPLES. 

/ 

1. It is required to lay out 120 acres in a rectanguiar 
form, the length of one side being given, equal 100 
perches. 

Acres. 

120 

4 

480 
40 



1,00)192,00 

192 Per. the length of the other side, 

2. The length of a rectangular piece of land is 8 
chains ; what must be its breadth, that the content may 
be 5 acres ? 

Ans. 6.25 chains. 



CHAP. IV." 1 LAYING OUT AND DIVIDING LAND. 16' 



PROBLEM III. 

To lay out a given quantity of land in a rectangular form, 
having the length to the breadth in a given ratio. 

RULE. 

As the less number of the given ratio, 
Is to the greater ; 
So is the given area, 
To a fourth term.* 

The square root of this fourth term will be the 
length required. Having the length, the breadth may 
be found by the preceding problem. Or it may be 
found in the same manner as the length. Thus, 

As the greater number of the given ratio, 

Is to the less ; 

So is the given area, 

To a fourth term. 

The square root of this fourth term will be the 
breadth required. 

EXAMPLES. 

1. It is required to lay out 864 acres in a rectangular' 
form, having the length to the breadth in the ratio of 
5 to 3. 



* Demonstration. Let ABCD, Fig. 85, be a rect- _ Fig. 85. 
angle, and ABFE and AHGD be squares on the 
greater and less sides respectively : then (1.6) AD 
: AE (AB) : : the rectangle AC : square AF. Also 
AB : AH (AD) : : the rectangle AC : square AG. 
ITence the truth of the rule is evident. 



168 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 

864 A. = 138240 P. 

Sq. P. Sq. P. 

As 3 : 5 : : 138240 : 230400 

V230400 =480 Perches, the length required. 

Sq. P. Sq. P. 

As 5 : 3 : : 138240 : 82944 

V82944 =288 Perches, the breadth required. 

2. It is required to lay out 27 A. 3 R. 20 P. in a rect- 
angular form, having the length to the breadth in the 
ratio of 9 to 7. Ans. Length 75.725 P. Breadth 58.897 P. 

PROBLEM IV. 

To lay out a given quantity of land in a rectangular 
form, having the length to exceed the breadth by a given 
difference. 

RULE. 

To the given area, add the square of half the given 
difference of the sides, and extract the square root of 
the sum ; to this root, add half the given difference for 
the greater side, and subtract it therefrom for the less.* 

Fig. 86. * Demonstration. Let ABCD, Fig. 86, be a 

..-r. rectangle ; in DC let DE be taken equal DA or 

/'' |\ BC, and let EC be bisected in F ; then (6.2) DF- 

j \ =DCXDE+FC 2 = DCXAD+FC 2 :=the rectangle 

AC+the square of half the difference of the sides 

DC, DA; also DF+FC = DC, the greater side, 

and DF— FC = DE or DA, the less side. 

This problem may be neatly constructed thus : 
take EC equal the given difference of the sides 
and bisect it in F ; make EG perpendicular to 
EC and equal to the square root of the given area, and with the centre F 
and radius FG describe the arc DG meeting CE produced in D : make DA 
perpendicular to DC and equal to DE, and complete the rectangle ABCD, 
which will be the one required. Since (47.1) FG 2 = EG 2 + EF 2 = the given 
area + the square of half the given difference of the sides, the truth of the 
construction is plain, from the preceding demonstration. 



CHAP. IV.] LAYING OUT AND DIVIDING LAND. 169 



EXAMPLES. 



1. It is required to lay out 47 A. 2 R. 16 P. in a rect- 
angle, of which the length is to exceed the breadth by 
80 perches. 

2)80 P. 47 A. 2 R. 16 P.=7616 Per. 
— 1600 
40 



40 y/ 9216=96 
half diff. add and subtract 40 



1600 



length 136 

breadth 56 

2. It is required to lay out 114 A. 2R. 33.4 P. in a rect- 
angular form, having the length to exceed the breadth 
by 15.10 ch. Ans. Length 42.25 ch. Breadth 27.15 ch. 

PROBLEM V. 

To lay out a given quantity of land in the form of a tri- 
angle or parallelogram, one side and an adjacent angle 
being given. 

RULE. 

For a triangle* 

As the rectangle of the given side and sine of the 

given angle, 
Is to twice the given area ; 
So is radius, 

To the other side, adjacent to the given angle. 
Then having two sides and the included angle given, 
the other angles and side, if required, may be found by 
trig, case 3. 

15 * 



170 



LAYING OUT AND DIVIDING LAND. [CHAP. IV. 



For a parallelogram. 

As the rectangle of the given side and sine of the 

given angle, 
Is to the given area ; 
So is radius, 
To the other side, adjacent to the given angle.* 

EXAMPLES. 

1. Let AB, BC, Fig. 87, be two 
sides of a tract of land ; the bear- 
ing of AB is S. 87*° W. dist. 16.25 
7 F ch. and the bearing of BC, N. 27 J° 
E. ; it is required to lay off 10 acres 
by a straight line AD, running from 
the point A, to the side BC. 
Bearing of BA, N. 87J° E. 
BC, N. 27* E. 




As ABXsin. B 



Angle B, 60° 
16.25 ch. - 
B, 60° - - 

twice the given area 200 sq. ch. 

: rad. 



CAB 

(sin. 



Ar. Co. 8.78915 
0.06247 

- - - 2.30103 

- - 10.00000 



: BD 14.21 ch. 



1.15265 



* Demonstration. It is demonstrated, prob. 3, chap. 3, Content of Land, 
that rad. : sin. B : : ABXBD : 2ABD (see Fig. 87) ; therefore (1.6 cor.) 
rad.XAB : sin. BXAB : : ABXBD : 2ABD, or (1G.5) sin. BXAB : 2ABD 
: : rad.XAB : ABXBD : : rad. : BD. Since ABDF is equal to 2ABD, 
the truth of the rule for the parallelogram is evident. 

This problem may be constructed as follows ; take AB equal the given 
side and draw BC making the angle B equal to the given angle ; make BE 
perpendicular to AB, and equal twice the given area of the triangle divided 
by the given side, or equal the given area of the parallelogram divided by 
the given side; and parallel to AB, draw EF cutting BC in D, and join 
DA ; then will ABD be the triangle required ; or complete the parallelo- 
gram ABDF, for the one required. The reason of the construction is plain. 



CHAP. IV".] LAYING OUT AND DIVIDING LAND. 171 

2. Given the side AB, Fig. 15, of a parallelogram, 
equal 20 ch. and the angle A 63° 30'; required the side 
AC, that the content may be 21i acres. 



a \r^ • A $AB20ch. Ar. Co. 8.69897 
AS Atf X sin. a j gin> A 63 o 3Q , 0.04821 

: the given area 215 sq. ch. 2.33244 

: : rad. 10.00000 



: AC 12.01 ch. ? 1.07962 

3. Given one side of a triangle, equal 30 perches, an 
angle adjacent to this side 71° 15', and the area 2 acres ; 
required the other side adjacent to the given angle. 

Ans. 22.53 perches. 

4. Given one side of a parallelogram, equal to 32.26 
ch., an angle adjacent to this side 83° 30', and the area 
74 acres ; required the other side adjacent to the given 
angle. Ans. 23.09 ch. 



PROBLEM VI. 

The area and base of a triangle being given, to cut off a 
given part of the area by a line running from the angle 
opposite the base. 

RULE. 

As the given area of the triangle, 

Is to the area of the part to be cut off; 

So is the given base, 

To the base corresponding to that area.* 

* The truth of this rule is manifest from 1.6. 



172 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 



EXAMPLES. 



Fi s- 8 C 8 - 1. Given the area of the triangle ABC, 

Fig. 88, equal 650 square perches, and 
the length of the base AB, 40 perches ; 
it is required to cut off 290 perches to- 
wards the angle A, by a line running from 




the angle C to the base. 

ABC. ADC. AB. AD. 

As 650 : 290 : : 40 : 17.85 per. 

2. In a triangle ABC, there are given the area 27 A. 
1 R 16 P. and the base AB 35.20 ch., to cut off 10 acres 
towards the angle B, by a line CD running from the 
angle C to the base : the part BD of the base is required. 

Ans. 12.87 ch. 
PROBLEM VII. 
The area and two sides of a triangle being given, to cut 

off a triangle containing a given area, by a line runn ing 

from a given point in one of the given sides, and falling 

on the other. 

RULE. 

As the given area of the triangle, 
Is to the area of the part to be cut off; 
So is the rectangle of the given sides, 
To a fourth term. 

Divide this fourth term by the distance of the given 
point from the angular point of the two given sides ; 
the quotient will be the distance of the required point 
from the same angle.* 

* Demonstration. From the demonstration to prob. 
3, chap. 3, we have, Fig. 89, rad. : sin. A : : ABx 
AC : 2ABC, and rad. : sin. A : : APxAG : 2APG; 
therefore (11 & 16.5) 2ABC : 2APG : : ABx AC: 
APxAG, or (15.5) ABC : APG : : ABxAC : APx 
b AG ; hence the truth of the rule is manifest. 




CHAP. IV.] LAYING OUT AND DIVIDING LAND. 173 



EXAMPLES. 

1. Given the area of the triangle ABC, Fig. 89, 5 
acres ; the side AB 50 perches, the side AC 40 perches, 
and the distance of a point P from the angle A, 36 
perches ; it is required to find a point G to which, if a 
line be drawn from the point P, it shall cut off a triangle 
APG containing 3 A. R. 20 P. 

As the triangle ABC 800 sq. p. Ar. Co. 7.09691 
: the triangle APG 500 2.69897 

• • ABxAC $ AB 50 L69897 

.AtfXAO£ AC 4Q 1.60206 

: APxAG 3.09691 

AP36 ------- log. 1.55630 

AG 34.72 per. 1.54061 

2. Given the area of a triangle ABC, 12 A. 1 R. 23 P. 

the side AB 20 ch., the side AC 16.25 ch., and the dis- 
tance of a point P in the side AB, from the angle A 8.50 
ch. ; it is required to find the distance AG of a point G 
in the line AC, so that a line drawn from P to G may 
cut off a triangle APG containing 3 acres. Ans. 9.25 ch. 

PROBLEM VIII. 

The area and base of a triangle being given, to cut of a 
triangle containing a given area, by a line running pa- 
rallel to one of the sides. 

RULE. 

As the given area of the triangle, 

Is to the area of the triangle to be cut off; 

So is the square of the given base, 

To the square of the required base. 



174 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 

The square root of the result will be the base of the 
required triangle.* 

EXAMPLES. 

Fi s- 90 c - 1. Given the area of the triangle 

ABC, Fig. 90, 500 square perches, and 
the base AB 40 perches ; it is required 
to cut off 120 sq. per. towards the angle 
A, by a line DG running parallel to the 



A- 




■\; /■■■' / 

e' -''' side BC. 



As the triangle ABC 500 - - - Ar. Co. 7.30103 
: the triangle ADG 120 2.07918 



AB 



JAB 40 1.60206 

[AB 40 1.60206 



: AD 2 2)2.58433 

AD 19.6 per. 1.29216 

2. Given the area of a triangle ABC, 10 acres, and 
the base AB 25 ch., to find BD a part of the base, so 
that a line DG running from the point D, parallel to 
the side AC, may cut off a triangle BDG containing 4i 
acres. Ana. BD = 16.77 ch.f 

* The truth of this rule is manifest from 19. G. 

This problem may be neatly constructed as follows : Let ABC, Fig. 90, 
be the given triangle, and AB the given base ; on AB describe the semi- 
circle AEB, and take AF to AB in the ratio of the part to be cut off, to 
the -whole triangle ; draw FE perpendicular to AB, meeting the semicircle 
in E, join AE, and make AD equal to AE ; from D draw DG parallel to 
BC, and the thing is done. For, join EB, and wc have, by similar triangles, 
AB : AE : : AE : AF ; therefore (20.6 cor. 2) AB : AF : : AB 2 : AE 2 (AD 2 ) 
: : [19.G] ABC : ADG. 

f If it be required to produce two sides of a given triangle so far that 
the triangle formed by these sides produced, and a line drawn between 
them parallel to the third side, may contain a given area, it may be done 
by the above rule. Thus, Fig. 90, ADG : ABC : : AD 8 : AB 2 . 



Fie. 91. 




CHAP. IV.] LAYING OUT AND DIVIDING LAND. 175 

PROBLEM IX. 

Tlie bearings of two adjacent sides 
AD, AE, Fig. 91, of a tract of land 
being given, to cut off a triangle 
ABC containing a given area by a 
line BC running a given course. 

RULE. 

From the given bearings of the lines, find the angles 
A, B, and C ; then, 

As the rectangle of the sines of the angles A and B, 

Is to the rectangle of radius and sine of the angle C ; 

So is twice the given area, 

To the square of the side AB.* 

In like manner the other sides may be found ; or 
having found one side, the others may be found by 
trig, case 1. 

EXAMPLES. 

1. Let the bearing of AD, Fig. 91, be N. 87° 30' E. 
and of AE, N. 27° 30' E. ; it is required to cut off 10 
acres by a line BC running N. 38° W. 

* The truth of this rule is evident from 
the demonstration to prob. 4, chap. 3. 

Construction. Draw AD, AE, (Fig. 92,) 
according to the given bearings, and in 
AD take AF equal the square root of the 
given area, and on it describe the square 
AFGH ; make IE = AI, and draw ED, 
according to the reverse bearing of the 
division line BC, meeting AD in D; on 
AD describe a semicircle, and produce 
GF to meet it in K, join AK and make 
AB equal to it ; draw BC parallel to DE, 
and ABC will be the triangle required. 
For join IF, EF and KD ; then (31.3, and K 

cor. 8.6) AD : AK (AB) : : AK (AB) : AF; or (cor. 19.6) AD : AF : : 
ADE : ABC ; but (1.6) AD : AF : : ADE : AFE; therefore (11.5) ADE : 
ABC : : ADE : AFE, and consequently (9.5) ABC = AFE; but because 
AI = IE, AFE = 2AFI = (41.1) AFGH; therefore ABC = AFGH=the 
given area of the triangle. 




176 



LAYING OUT AND DIVIDING LAND. [CHAP. IV. 



AD, N. 87° 30' E. 

AE, N. 27 30 E. 



BA, S. 87° 30' W. 
BC, N. 38 00 W. 



CA,S.27°30'W. 
CB, S. 38 00 E. 



Angle A, 60 00 



125 30 Angle C, 65 30 
180 00 



As sin. AX sin. B, 
: rad. X sin. C, 



Angle B, 54 30 

A 60° 00' 
B 54 30 

C 65 30 
rad. 



Ar. 



: : twice the given area, 200 sq. ch. 
: AB 2 • 



Co. 0.06247 

— 0.08931 

9.95902 

- 10.00000 

- 2.30103 

- 2)2.41183 



AB 16.07 1.20591 

2. Given the bearing of one side of a tract of land, 
S. 53° 15' E., and the bearing of an adjacent side taken 
at the same angle, N. 55° 00' E., to cut off 4 acres by a 
line running N. 4° 00' ~W\; required the distance on the 
first side. 



Fig. 93 



Ans. 9.76 ch. 

PROBLEM X. 

The bearings of three adjacent 
sides, EA, AB, BF, Fig. 93 
or 94, of a tract of land, and 
the length of the middle side 
AB, being given, to cut off a 
trapezoid ABCD, containing 
a given area, by a line DC, 
parallel to AB. 

K 

RULE. 

From the given bearings find the angles A and B ; 
add these together, and take the difference between 
their sum and 180°, and call it P. Then, 
As the product of the sines of A and B, 
Is to the product of radius and sine of P ; 




CHAP. IT.] LAYING OUT AND DIVIDING LAND. 



177 



So is twice the area to be cut off, 

To a fourth term. 
When the sum of the angles A and B is greater than 
180°, add this fourth term to AB 2 ; but when the sum of 
these angles is less than 180°, take the difference between 
this fourth term and AB 2 . The square root of the re- 
sult will be DC. Then, 

As the sine of P, 

Is to the sine of B, 

So is the difference between DC and AB, 

To AD * 



* Demonstration. Produce EA and FB, Fig. 95, to meet in P. Then 
(19.6) PDC : PAB : : CD 2 : AB 2 , or (17.5) ABCD : PAB : : CD 2 — AB 2 
: AB 2 , or (A.5) PAB : ABCD : : AB 2 : CD 2 — AB 2 , or (15.16.5) 2PAB : 
AB 2 : : 2ABCD : CD 2 — AB2. But by the demonstration to prob. 4, chap. 3, 
2PAB : AB 2 : : sin. AXsin. B : rad.Xsin. P. Consequently, (11.5) 
sin. AXsin. B : rad,X s in. P : : 2ABCD : CD 2 — AB 2 . 
Fig. 94. 13 Fig. 95. F 





Now it is plain that 
AB 2 , added to this 4th 
term, gives CD 2 . A p 
similar demonstration 
applies when the sum of the angles A and B is less than 180°, as in Fig. 94. 
The latter part of the rule does not require demonstration. 

Construction. Draw AI, Fig. 93, perpendicular to AB, and make it equal 
to the quotient of twice the given area divided by AB. From I, draw IH 
parallel to AB meeting AE and BF, in G and H, and on GH, describe the 
semicircle GMH. From A, draw AL parallel to BF ; and make LM perpen- 
dicular to GH. With the distance HM and centre H, describe the arc MN ; 
and from N, draw ND parallel to AL. Lastly, draw DC parallel to AB, and 
it will be the division line required. For join BD, BG, and CG, Fig. 95. 
Then by similar triangles PG : PD : : GH : DC : : GH : HM : : HM 
: HL : : DC : AB : : PC : PB. Hence (3.6) CG is parallel to BD ; and 
consequently the triangle BDC is equal to BGD. To each of these, add ABD. 
Then we have ABCD = ABG. But it is plain from the construction that 
ABG is equal to the given area. Hence ABCD is equal to the given area. 

When the sum of the angles A and B is less than ISO , as in Fig. 94, 
Z 



178 LAYING OUT AND DIVIDING LAND. 



EXAMPLES. 



1. Given the bearing of EA, Fig. 93. West, AB, N. 
10° E. dist. 15 ch. ; and BF, N. 58° 30' E. to cut off 10 
acres by a line CD, running parallel to AB. Required 
the length of the division line and the distance AD. 



"&■ 



AE, N. 90° E. BF, N. 58° 30' E. A, 80° 0' 

AB, N. 10 E. BA, S. 10 W. B, 131 30 



80° 48° 30 211 30 

180 180 



B=131 30 P=31°30' 



As sin Ay sin B $ A ' 80 ° 00 ' Ar ' Ca a00665 
As sin. A X sin. tf,^ 131 30 0.12554 



Rad. x sin 



•-• 



Rad. 10.00000 

P, 31 30 - - - - 9.71809 

: : twice the given area 200 sq. ch. - - - 2.30103 

fourth term 141.68 2.15131 

AB 2 r=:225. 



DC =V / 366.68= 19.15 ch. 

As sin. P, 31° 30' - - Ar. Co. 0.28191 

: sin.B, 131 30 9.87446 

: : DC— AB, 4.15 0.61805 



AD 5.95 0.77442 



the semicircle must be described on AB ; the point L must be deter- 
mined by drawing GL parallel to FB : and the arc MN must be described 
with the radius BM and centre B. The other parts of the construction are 
the same as before. 



CHAP-. IV.] LAYING OUT AND DIVIDING LAND. 179 

2. Given the bearings of three adjacent sides of a 
tract of land and the length of the middle one as follows : 
1st. N. 20° W. ; 2d. N. 60° 30' E. dist. 6 ch. ; 3d. S. 61° 
30' E. ; to cut off a lot containing 21 acres, by a line 
parallel to the 2d side. Kequired the length of the 
division line and the distance on the 1st side. 

Aiis. Division line 8.70 ch. ; distance on 1st 
side 3.45 ch. 

3. Given as follows : 1st side N. 31° 15' W.; 2d N. 
58° 45' E. dist. 13.50 ch. ; 3d S. 14° 45' E. ; to cut off 8 
acres by a line parallel to the 2d side. The length of 
the division line and the distance on the 1st side are 
required. Ans. Division line 11.61 ch. ; distance 

on the 1st side 6.38 ch. 

PROBLEM XI. 

The hearings of three adjacent sides Fi S- 96 - J 

EA, AB, BF, Fig. 96, of a tract h/^ 

of land, and the length of the c>^^ Vs - x -- 
middle side AB being given, to 
cut off a trapezium, ABCD, con- 
taining a given area, by a line 
CD, running a given course. 

RULE. u"— E 

Draw AS parallel to BF, meeting CD or CD pro- 
duced, in S. From the given bearings, find the interior 
angles A, B, C, and D ; add A and B together, and take 
the difference between their sum and 180°, and call 
it P. Then, 

As the product of the sines of C and D, 
Is to the product of radius and sine of P; 
So is twice the area to be cut off, 
To a fourth term. 



180 



LAYING OUT AND DIVIDING LAND. [CHAP. IV. 



Also, as the product of the sines of C and D, 
Is to the product of the sines of A and B ; 
So is AB 2 , 
To a fourth term. 

When the sum of the angles A and B, is greater 
than 180°, add these two fourth terms together; but 
when the sum of these angles is less than 180°, take 
the difference of the fourth terms. The square root 
of the result will be CD. Then, 

As sin. C : sin. B : : AB : CS. 
The difference between CD and CS, gives DS. Then, 
As sin. P : sin. C : : DS : AD* 




Fig- 97. f * Demonstration. Produce 

EA and FB, Fig. 97, to meet in 
P ; draw AR and BU, each pa- 
rallel to CD, and let VW, also 
parallel to CD, make the trian- 
gle PVW equal to PAB, Then 
(15.6) PA : PV: : PW r : PB; 
but (4.6) PA : PV : : AR 
VW, and PW : PB : : VW 
BU. Therefore (11.5) AR 
VW : : VW : BU, and hence 
(17.6) ARXBU=VW 2 . But by trigonometry, 

As sin. ARB (sin. C) : sin. B : : AB : AR, 
sin. AUB (sin. D) : sin. A : : AB : BU. 

Hence (23.6) As sin. CXsin. D : sin. AXsin. B : : AW : ARXBU; 

Or, sin. CXsin. D : sin. AXsin. B : : AB 2 : VW 8 . 
And by the demonstration to the rule in the last problem, Ave have 
sin. CXsin. D : rad.Xsin. P : : 2VWCD (2ABCD) : CD 2 — VW 2 . 
The sum of these fourth terms gives CD 2 . The demonstration is similar, 
when the sum of the angles A and B is less than 180°. 

Construction. From B, Fig. 96, draw BU according to the reverse bear- 
ing of the division line DC, meeting EA or EA produced in U. Make AI 
perpendicular to AB, and equal to the quotient of twice the given area, divi- 
ded by AB. Draw IG parallel to AB ; Gil parallel to BU ; and UL parallel 
to BF. On GH, describe the semicircle GMII, and make LM perpendicular 
to GH ; with the radius HM and centre H, describe the arc MN ; and from N, 
draw ND parallel to UL. From D, draw the division line DC parallel to BU. 



CHAP. IV.] LAYING OUT AND DIVIDING LAND. 



181 



EXAMPLES. 

1. Let the bearings of EA, Fig. 96, be N. 80° 30' W. ; 
AB, North, dist. 12 ch. : and BF, N. 58° E. ; it is re- 
quired to cut off 10 acres by a line DC, running N. 14° 
30' W. 

AE, S. 80° 30' E. BF, N. 58° E. CB, S. 58° 00' W. 
AB,N. 00 K BA,S. E. CD, S. 14 30 E. 

80 30 58 C=72°30' 

180 180 

A= 99° 30 / B=122 

DA, N. 80° 30' W. A = 99° 30* 

DC,N. 14 30 W. B=122 00 

D=66°00' 221 30 

180 00 

P=41 30 

Aa *; n rv,™ n $ C, 72° 30* - - - Ar. Co. 0.02058 
As sin. Cxsni. D | D ' 66 0Q 03927 

, ^ • p \ rad. 10.00000 

: rad.xsm. r, ^ 4130 9.82126 

: : twice the given area 200 sq. ch. - - - 2.30103 
. fourth term 152.1 - 2.18214 



When the sum of the angles A and B is less than 180°, the semicircle 
must be described on BU ; the point L must be determined by drawing GL 
parallel to BF, and the arc MN must be described with the radius BM and 
centre B. 



The demonstration is exactly the same as that for the construction of the 
last problem. 
16 



182 LAYING OU AND DIVIDING LAND. [CHAP. IV. 

As sin. Cxsin. D, < ^ 



sin. A x sin. B, 
:AB 8 



72° 30' Ar. Co. 0.02058 

66 00 - 0.03927 

A 99 30 9.99400 

B 122 00 9.92842 

AB 12 1.07918 

AB 12 1.07918 



: fourth term 138.24 2.14063 

fourth term 152.10 



00=^290.34=17.04 

As sin. C 72° 30' Ar. Co. 0.02058 

: sin. B 122 00 9.92842 

::AB12 1.07298 

: CS 10.67 1.02818 

DC 17.04 



DS 6.37 

As sin. P 41° 30* ------ Ar. Co. 0.17874 

: sin. C 72 30 .-- 9.97942 

: : DS 6.37 ----- 0.80414 



: AD 9.17 - - - - - - - - - - - 0.96230 

2. Given the bearings of three adjacent sides of a tract 
of Jand and the length of the middle one as follow: 1st. 
N. 31° 15' W.; 2d. N. 58° 45' E. dist. 13.50 ch.; 3d. S. 
14° 45' E.; to cut off 8 acres by a line from the 1 st. side 
to the 3d. running S. 87° 30' E. ; requirea the length of 
the division line and the distance on the 1st side. 

Ans. Division line 12.76 ch. ; distance 
1st. side 2.69 ch. 

3. Given as follow ; 1st side, N. 74° 45' W. ; 2d. N. 
37° E. dist. 17.24 ch. ; 3d. N. 84° E. ; to cut off a field 
containing 20 acres, J>y a line from the 1st. side to the 3d. 



CHAP. IV.] LAYING OUT AND DIVIDING LAND. 



183 



running N. 20° E. The length of the division line and 
the distance on the 1st side are required. Ans. Division 
line 19.68 ch. ; distance on 1st side 14.01 ch. 

PROBLEM XII. 

TJiebearings of several adjacent sides, EA, AY, VW, WX, 
XB, BF, Fig. 98, of a tract of land, and the distance of 
each, except tlie first and last, being given, to cut off a 
given area, by a line DC, running a given course. 

RULE. 

Join AB and calculate the area of AY WXBA, and 
the bearing and distance of AB. Subtract the area of 
AYWXBA from the area to be cut off, the remainder 
will be the area ABCD. Then with the bearings of 
EA, AB, BF, DC, the distance AB, and the area of 
ABCD, proceed as in the last problem. 

EXAMPLES. ? Fi 2- 98 ' 

1. Let the bearing 
ofEA,Fig.98,beN. 
48° 30' W.; AY,S." 
78° W.dist. 8 ch.; 
VW, N. 26° 30' W. 
dist. 11.08 ch.;WX, 
N. 38° 30' E. dist. 
12.82 ch.; XB, S. 
64° E. dist. 10.86 
ch. ; and BF, S. 86° E. It is required to cut off 30 
acres by a line DC, running N. 32° 15' E. 




Stat. 


Bearing. 


Dist. 


N. 


S. 


E. 


W. 


E. D.D. 


W.D.D. 


Multi- 
pliers. 


N.Ar. 


S. Areas. 


AV 


S. 78° W 


8.00 




1.66 




7.83 




12.79 


0.00 E 






VW 


N. 26£W 


11.08 


9.91 






4.95 




12.78 


12.78 W 




126.6498 


WX 
XB 


N. 38^ E 


12.82 


10.03 




7.98 




3.03 




9.75 W 




97.7925 


S. 64 E. 


10.86 




4.76 


9.76 




17.74 




7.99 E 




38.0324 


BA 








(13.52) 




(4.96) 


4.80 




12.79 E 




172.9208 








19.94 


19.94 


17.74 


17.74 


25.57 


25.57 


Sq. 


ch. 


2 


435.3955 
17.69775, 



184 LAYING OUT AND DIVIDING LAND. [dlAP. IV. 

3q. ch. 

Area to be cut off 300. 
Area of AVWXBA 217.69775 

Area of ABCD 82.30225 

As diff. of lat. of BA, 13.52 S. Ar. Co. 8.86902 

: dep. do. - - 4.96 W. 0.69548 

::rad. - 10.00000 

: tang of bearing of BA, S. 20° 9' W. - - - 9.56450 

Asrad. Ar.Co. 0.00000 

: sec. of bearing 20° 9' 10.02743 

:: diff. of lat. 13.52 1.13098 

: BA 14.40 1.15841 

The angles, found from the bearings, are A=lll° 21', 
B=106° 9', C=61° 45', D=80° 45' and P=37° 30'. 



a • n,' r^C,61° 45'- - -Ar.Co. 0.05508 
As sin. C x sin. D < ^' g0 l 



45 - - 0.00568 



• radvsin P \ md ' 10.00000 

. raa.xsm. r, J p ? 37 30 9.78445 

: : twice the area ABCD 164.6 sq. ch. - - 2.21643 

: fourth term 115.25 2.06164 



As sin. Cxsin. D, \ ^ g() ^ " r ' 

S K HI 
\B, 106 
X AB, 14 
\ AB, 14 



0.05508 

0.00568 

. . - R (A, 111 21 - - - - 9.96912 

Bin.AXBin.JJ, j B , 106 9 - - - - 9.98251 

AR2 X AB, 14.40 - - - - 1.15836 

^.40 --.. 1.15836 



fourth term 213.36 2.32911 

do. 165.25 

DC=v/ 328.61 = 18.13 



CHAP. IV.] LAYING GUT AND DIVIDING LAND. 



185 



As sin. C, 61° 45' Ar. Co. 0.05508 

: sin. B, 106 9 ------ - 9.98251 

: : AB, 14.40 1.15836 



: CS, 15.70 1.19595 

As sin. P, 37° 30' Ar. Co. 0.21555 

: sin. C. 61 45 9.94492 

: : DS, 2.43 0.38561 



: AD, 3.52 0.54608 

2. Given as follow; 1st side, N. 62° 15' W. ; 2d N. 
19° E. dist. 18 ch. ; 3d S. 77° E. dist. 15.25 eh. ; 4th S. 
27° E. ; to cut off 35 acres by a line, from the first side 
to the last, running N. 82° 30' E. Kequired the length 
of the division line, and the distance on the first side. 
Ans. Division line 22.98 ch. ; distance on 
1st side 5.14 ch. 



PROBLEM XIII. 



The bearings of seve- Fi s- "• 

ral adjacent sides, 
AB, BC, CD, DE, 
Fig. 99, of a tract 
of land, and the 
distance of each, ex- 
cept the last, being 
given, to cut off a 
given area by a line 
AH running from b 
the angle A, and 
falling on the side 
DE. 

RULE. 

By Prob. 9, chap. 
1, change the bear- 
ings of all the given sides, so as to make the side, on 
which the division line is to fall, a meridian. 
16* 2A 




186 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 

With the given distances and changed bearings, find 
the corresponding differences of latitude and departures; 
add together the numbers in each departure column, and 
take the difference of their sums, which will be the de- 
parture of the division line, and must be placed in the 
proper column, opposite said line. Then having all the 
departures, find the double departures, as in Prob. 11, 
of the last chapter. Find also the multipliers, beginning 
with the one to correspond with the division line, and 
assuming it ; multiply the known differences of latitude 
by their corresponding multipliers, and place the pro- 
ducts in the proper columns of north and south areas. 

Add together the products in each of the columns of 
areas, and subtract the less sum from the greater ; take 
the difference between the remainder and double the area 
to be cut off, and divide it by the multiplier correspond- 
ing to the side on which the division line is to fall ; the 
quotient will be the difference of latitude of this side, 
which place against it, in the column of north or south 
latitude, according as its changed bearing is north or 
south. Then add together the numbers in each latitude 
column, and take the difference of their sums, which will 
be the difference of latitude of the division line, of the 
same name with the less sum. 

With the difference of latitude and the departure of 
the division line, find, by Prob. 10, chap. 1, its changed 
bearing and its distance. Then find the true bearing 
by note to the rule in Prob. 9, chap. 1* 

EXAMPLES. 

1. Let the bearing of AB be N. 62i° W. 14.75 ch. ; BC, 
N. 19° E. 27 ch. ; CD, S. 77° E. 22.75 ch. ; and DE, S. 27° 
E. ; it is required to cut off 70 acres by a line AH, run- 
ning from the angle A and falling on the side DE. 

* The reason of this rule is sufficiently obvious without a demonstration. 



CHAP. IV.] LAYING OUT AND DIVIDING LAND. 



187 







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As diff. lat. of HA, 5.22 S. - 
dep. do. 28.33 W. - 
rad. 



tang, changed bear, of HA, S. 79° 34' W. 
Subtract 27 00 



Ar. Co. 9.28233 
• - - 1.45225 
■ - - 10.00000 



1073458 



True bearing of HA, S. 52 34 W. 



188 



LAYING OUT AND DIVIDING LAND. [CHAP. IV. 



As rad. Ar. Co. 0.00000 

: sec. changed bearing of HA, 79° 34' - -10.74210 
: : diff. lat. 5.22 0.71767 



: dist. AH, 28.83 1.45977 

Hence AH, bears N. 52° 34' E. dist. 28.83 ch. 

2. Given as follow : 1st side S. 78° W. 8 ch. ; 2d N. 
26 h° W. 11.08 ch. ; 3d N. 38£° E. 12.82 ch.; 4th S. 64° 
E. 10.86 ch. ; 5th S. 23£° E. ; to cut off 25 acres by a 
line running from the place of beginning, and falling 
on the 5th side ; required its bearing and distance. 
Ans. N. 45° 1' E. dist. 10.67 ch. 



Fig. 100. 



PROBLEM XIV. 

The sides AB, BC, CA, Fig. 100, of 
a triangular piece of ground being 
given, to divide it into two parts 
having a given ratio, by a line FE, 
running parallel to one of the sides 
cwBC. 

RULE. 

As the sum of the numbers expressing the ratio of the 

parts, 
Is to that number of the ratio which corresponds to the 

part to be adjacent to A; 
So is the square BC, 
To the square of FE. 

Then, As BC : AB : : FE 




AF.* 



* Demonstration. Let m to n be the ratio of the part AFE to the part 
FECB ; then (18.5) m + n : m : : ABC : ADE : (19.6) BC 2 : FE 2 . 

Construction. On AB describe the semicircle AMB, and by Prob. 17, 
Page 36, divide AB in K, so that AK may be to KB in the given ratio of the 
part AFE to the part FECB ; draw KM perpendicular to AB, meeting the 



CHAP. IV.] LAYING OUT AND DIVIDING LAND. 189 



EXAMPLES. 

1. Let AB be 21.26 ch. ; BC, 12.76 ch. ; and AC, 
19.30 ch. ; it is required to divide the triangle by the 
line FE, parallel to BC, so that the part AFE may be 
to the part FECB as 2 to 3. 

As 5 : 2 : : 12.76 2 : FE 2 = 65.12704. 

FE=V 65.12704 = 8.07. 
As 12.76 : 21.26 : : 8.07 : AF = 13.45. 

2. The three sides of a triangular piece of land, taken 
in order, measure 15, 10, and 13 chains respectively ; it 
is required to divide it into two equal parts by a line 
parallel to the second side. What will be the length 
of the division line and its distance from the place of 
beginning, measured on the first side ? 

Am. Division line 7.07 ch. ; dist. on 1st side 10.61 ch. 



PROBLEM XV. 

The bearings and distances of the 
sides AB, BC, CA, Fig. 101, of a 
triangular 'piece of ground being 
given, to divide it into two parts 
having a given ratio, by a line FE, 
running a given course. V. \\/^/ 

RULE. 

As the product of the sines of F and E, 
Is to the product of the sines of B and C ; 

semicircle in M, and \rith the radius AM and centre A, describe the are 
MF. From F, draw the division line FE parallel to BC. Since, (35.3, and 
cor. 8.6) AB : AM (AF) : ■ AM (AF) : AK, we have (20.6 cor. 2) AB : AK 
: : AB 2 : AF 2 : : ABC : AFE. Hence the truth of the construction is evident. 




190 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 

So is the square of BC, 

To a fourth term. 
Multiply this fourth term by that number of the 
ratio which corresponds to the part to be adjacent to 
the angle A, and divide the product by the sum of the 
numbers expressing the ratio. The square root of the 
result will be FE. Then, 

As sin. A : sin. E : : FE : AF * 



EXAMPLES. 

1. Let the bearing of AB, be S. 82i° E. dist. 14.17 
ch.; BC, N. 181° W. 8.51 ch.; and CA, S. 61i° W. 
dist. 12.87 ch.; it is required to divide the triangle by 
the line FE, running N. 141° E. so that the part AFE 
may be to the part FECB in the ratio of 2 : 3. 

* Demonstration. Draw CG and BR, Fig. 
102, parallel to EF ; and let VW, also parallel 
to EF, make the triangle AVW equal to ABC. 
Then (15.6) AB : AV : : AW : AC ; but (4.6) 
AB : AV : : BR : VW, and AW : AC : : VW : 
GC. Therefore BR : VW : : VW : GC ; and 
hence (17.6) BRXGC = VW 3 . But by trigo- 
\ X "; /,/'/ " nometry, 

v -0:i^''' As sin - R ( sin - E ) : sin - C : : BC : BR, 

M sin. G (sin. F) : sin. B : : BC : GC. 

Hence (23.6) sin. EX sin. F : sin. BXsin. C : : BC a : BRXGC : : BC 2 : 
VW 2 . 

Also, m+n : m : : ABC : AFE : : AVW : AFE : : (19.6) VW 2 : FE 3 . 

Construction. From C, Fig. 101, draw CG according to the reverse bear- 
ing of FE, and on AG describe the semicircle AMG. By prob. 17, page 
36, divide AB in K, so that AK may be to KB in the given ratio of the 
part AFE to the part FECB. Draw KM perpendicular to AB, and with 
the radius AM and centre A, describe the arc MF. From F, and parallel 
to GC, draw FE the required division line. For join KC, Fig. 102 ; tfien 
(1.6) KC divides the triangle in the given ratio. Now AC : AE : : AG : 
AF (AM) : : (cor. 8.6) AM (AF) : AK ; therefore (11.5) AC : AE : : AF 
: AK, and hence (15.6) the triangle AFE is equal to AKC. Consequently 
FE divides the triangle in the given ratio. 



CHAP. IV.] LAYING OUT AND DIVIDING LAND. 191 

Angle A=36£°, B=63 i°. C=80i° ? E=46l° and F=83° 

A . ™ v . tj, fE,46°45 / AR. Co. 0.13765 

As sin. E X sin. F, j p | g3 0Q 0Mm 

j B, 63 30 9.95179 

1 C, 80 15 9.99368 

J BC, 8.51 0.92993 

{BC, 8.51 0.92993 



sin. B X sin. C, 
:BC 2 , 



: fourth term 88.35 1.94623 

2 



5)176.70 



FE=V 35.34=5.95 

As sin. A, 36° 15' Ar. Co. 0.22819 

: sin. E, 46 45 9.86235 

: : FE, 5.95 0.77379 



: AF, 7.32 0.86433 

2. The bearings and distances of a triangular piece of 
land ABC are, AB, S. 69° E. 21.40 ch. ; BC, N. 31 J E. 
18.66 ch. ; and CA, S. 74i W. 30.85 ch. • and it is re- 
quired to divide it by a line FE, running due north, so 
that the part AEF, may be to the part FECB, as 4 to 5. 
"What will be the length of the division line FE, and 
the distance AF? Ana. FE 10.74, and AF 17.40. 

PROBLEM XVI. 

The bearings and distances of Fi s- 103 

the sides AB, BC, CD, DA, 
Fig. 103, of a trap>ezoidal 
tract of land being given, to 
divide it into two parts having 
a given ratio, by a line FE, 
running parallel to the paral- 
lel sides AB, CD. 

RULE. 

Multiply the square of AB, by that number of the 




192 LAYING OUT AND DIVIDING LAND. [dlAP. IV. 

ratio which corresponds to the part, to be adjacent to CD, 
and the square of CD, by the other number of the ratio. 
Add the two products together, and divide the sum by 
the sum of the numbers expressing the ratio. The 
square root of the quotient will give FE. Then, 
As DC— AB : FE— AB : : AD : AF. ::: 

EXAMPLES. 

1. Let the bearing of AB be N. 14° E. dist. 10 ch. BC, 
N. 55£° E. dist. 18.67 ch. ; CD, S. 14° W. dist. 20.98 ch. ; 
and DA, W. 12.70 ch. ; it is required to divide the trape- 
zoid into two parts by a line FE, parallel to AB or DC, 

Fig. 104. c * Demonstration. Produce DA 

and CB, Fig. 104, to meet in P. 
Then (19.6) PDC : PAB : : CD 2 
AB 2 , or (17.5) ABCD : : PAB : 
CD 2 — AB 2 : AB 2 , or (16.5) ABCD 
CD 2 — AB 2 : : PAB : AB 2 . In like 
manner ABEF : FE*— AB 2 : : PAB 
: AB 2 . Hence (11.5) ABCD : CD* 
* u A K v D _AB 2 : : ABEF : FE 2 — AB 2 , or 

(16.5) ABCD : ABEF : : CD 2 — AB* : FE 2 — AB 2 . Therefore m + n : m : : 
CD 2 — AB 2 : FE 2 — AB 2 , or multiplying extremes and means, m + n FE 2 — 
m + n. AB 2 =to. CD 2 — to. AB 2 . But (m + n.) AB 2 = to. AB 2 + n. AB 2 . There- 
fore, adding equals to equals, we have m + n. FE 2 =to. CD 2 + n. AB 2 . Hence 
the truth of the rule is evident. 

Construction. Join CA, Fig. 103, and parallel to it, draw BH, meeting 
DA produced in H. Divide (prob. 17, page 36) HD in K so that UK may be 
to KD in the given ratio of ABEF to FECD, and draw KL parallel to BC. 
On CD, describe the semicircle CMD, and draw LM perpendicular to CD. 
With the radius CM and centre C, describe the arc MN, and from N draw 
NF parallel to KL. From F, draw the division line FE parallel to AB or 
CD. For join KC, Fig. 104, and draw KU parallel to AB. Then since BH is 
parallel to AC, the triangle AHC is equal to ABC ; and adding ADC to each, 
we have CHD=ABCD. Now (4.6) PC : PE : : CD : FE (CM) : : (cor. 8.6) 
CM (EF) : CL (UK) : : PF : PK. Therefore (11.5) PC : PE : : PF : PK; 
and hence (15.6) the triangle PEF is equal to PCK, Consequently CKD 
= FECD. But it has been proved that CHD = ABCD; hence taking 
equals from equals we have TICK = ABEF. But (1.6) HCK : CKD : : 
HK : KD : : m : n. Therefore ABEF : FECD : : to : n. 




T' V M 



CHAP. IV.] LAYING OUT AND DIVIDING LAND. 



193 



so that the part ABEF may be to the part FECD as 
3 to 2. 

2. AB 2 =200 
3. CD 2 =1320.4812 



5)1520.4812 

FE= V304.0962 =17.44 
As 10.98 : 7.44 : : 12.70 : AF = 8.61 

2. The boundaries of a trapezoidal field ABCD are 
given as follow ; viz. AB, N. 80° "W. 60 per.; BC, N. 391° 
W. 45.5 per.; CD, S. 80° E. 89.4 per.; and DA, South, 
30 per. ; and it is required to divide it into two equal 
parts by a line FE parallel to AB or CD. What will be 
the length of the division line FE, and the distance AF? 
Ans. FE 76.13 per., and AF 16.46 per. 



PROBLEM XVIL 

The hearings and distances of the 
sides AB, BC, CD, DA, Fig. 105, 
of any quadrilateral tract of land 
being given, to divide it into two 
parts having a given ratio, by a line 
FE, running parallel to one of the 
as AB or CD. 



Fiff. 105 




RULE. 

Call the side to which the division line is to be paral- 
lel, the parallel side ; and the one opposite to this, the 
opposite side. From the bearings, find the angles. Take 
the difference between the sum of the angles adjacent 
to the parallel side and 180°, and call it P. Then, 
17 2B 



194 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 

As the product of the sines of the angles adjacent to 
the parallel side, 

Is to the product of the sines of the angles adjacent 
to the opposite side : 

So is the square of the opposite side, 

To a fourth term. 

Multiply this fourth term by that number of the ratio 
which corresponds to the part to be adjacent to the 
parallel side, and to the product add the product of the 
square of the parallel side by the other number of the 
ratio ; and divide the sum by the sum of the numbers 
expressing the ratio. The square root of the quotient 
will be the length of the division line FE. Then, 

As the sine of P, 
Is to the sine of E ; 

So is the difference between FE and the parallel side, 
To the distance of F from the adjacent end of the 
parallel side.* 

* Demonstration. Produce DA 
and CB, Fig. 106, to meet in P. 
Draw DR and CG each parallel to 
AB ; and let VW, also parallel to 
AB, make the triangle PVW equal 
to PCD. Then (15.G) PD : PV : 
PW : PC. But (4.G) PD : PV : 
DR : VW, and PW : PC : : VW 

CG. Therefore (11.5) DR : VW : : VW : CG ; and hence (17.6) DRXCG 

= VW 2 . But by trigonometry, 

As sin. CRD (sin. B) : sin. C : : CD : DR. 
sin. CGD (sin. A) : sin. D : : CD : CG. 

Hence (23.6) sin. AX sin. B : sin. CXsin. D : : CD 2 : DRXCG. 
Or, sin. AX sin. B : sin. CX s i n . D : : DC 2 : VW"-. 

But by the demonstration to the rule in the last problem, we have 

m + n. FE 2 = m. VW 2 + n. AB 2 . 
Hence the truth of the rule is evident. 

Construction. From C, Fig. 105, draw CG parallel to AB, and on it de- 
scribe the semicircle CMG. 




CHAP. IV. J LAYING OUT AND DIVIDING LAND. 195 



EXAMPLES. 

1 Let the bearing of AB be North, 12 ch. ; BC, N 
56£° E. 20.78 ch. ; CD, S. 33|° E. 22.21 ch. ; and DA, S. 
80^° W. 30 ch. j it is required to divide the tract into 
two parts by a line FE, parallel to AB, so that the part 
ABEF may be to the part FECD as 3 to 5. 

Angle A=80£ o , B=123F, C=90°, D=66°, and P=24°. 

a oc v, a^ • t? $ A > 80 ° 30 ' Ar. Co. 0.00600 
as sin. ax sin. tf, ^ u3 3Q _ 0.07889 

•sinCvsinD $ C, 90 00 - - - - 10.00000 
. sin. ox sin. u, ^ 66(K) 9.96073 

™ 2 ( CD, 22.21 1.34655 

..uu } CD, 22.21 1.34655 

: fourth term 547.92 2.73872 

3 



1643.76 
5AB 2 =720.00 



8)2363.76 

FE=v/ 295.47= 17.19 
As sin. P, 24° 00' Ar. Co. 0.39069 

: sin. E, 123 30 9.92111 

: : FE-AB, 5.19 0.71517 



: AF, 10.64 1.0269', 



Join CA, and draw BH parallel to it meeting 1 DA produced in H. Divide 
HD in K, so that HK may be to KD in the given ratio of the part ABEF to 
FECD. Draw KL parallel to BC and LM perpendicular to CG. With the 
radius CM and centre C, describe the arc MN. Draw NF parallel to KL 
and FE parallel to AB. Then will FE be the division line. When the di- 
vision line is to be parallel to CD, the semicircle must be described on CD ; 
and the line CG need not be drawn. The demonstration of the construction 
13 the same as for the last problem. 



196 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 

2. The boundaries of a field ABCD are given as fol- 
low : viz. AB, S. 101° W. 7.20 ch. ; BC, S. 67° W. 12.47 
ch. ; CD, N. 23° W. 13.33 ch. ; and DA, S. 89° E. 18 ch. ; 
and it is to be divided into two parts by a line FE, paral- 
lel to the side AB, so that the part ABEF may be to the 
part FECD, as 3 to 4. Required the length of the divi- 
sion line FE, and the distance AF. 

Am. FE 10.69 ch. ; and AF 7.15 ch. 

3. Given the boundaries of a field the same as in the 
preceding example, to divide it into two parts by a line 
FE, parallel to the side CD, so that the part ABEF may 
be to the part FECD, as 3 to 4. Required FE and AF. 

Ans. FE 10.14, and AF 10.16. 

PROBLEM XVIII. 

The bearings and distances of the 
sides AB, BC, CD, DA, Fig. 
107, of any quadrilateral trad 
of laud, being given, to divide it 
into two parts having a given 

ratio by a line FE, running a given course from some 

point in AD to another in BC. 

RULE. 

From A, draw AS parallel to BC, meeting FE in S. 
From the bearings find the angles A, B, C, D, E, and F.* 
Take the difference between the sum of the angles A 
and B, and 180°, and call it P. Then, 
As the product of the sines of the angles E and F, 
the product of the sines of the angles A and B ; 
the square of AB, 
a fourth term. 
Also, As the product of the sines of the angles E and F, 
: the product of the sines of the angles C and D ; 

* It is immaterial whether it is the angle BEF or CEF, that is found, 
also whether, AFE or DFE. 




CHAP. IV."] LAYING OUT AND DIVIDING LAND. 197 

: : the square of CD, 

: to a fourth term. 
Multiply this latter fourth term by that number of the 
ratio which corresponds to the part to be adjacent to AB, 
and the other fourth term by the other number of the 
ratio ; add the two products together, and divide the sum 
by the sum of the numbers expressing the ratio. The 
square root of the quotient will give the length of the di- 
vision line FE. Then, 

As sin. E. : sin. B : : AB : ES. 
The difference between FE and ES, gives FS. Then, 
As sin. P. : sin. E : : FS : AF.* 

EXAMPLES. 

1. Let the bearing of AB be North, dist. 12 ch.; BC 
N. 56i° E. 20.78 ch.; CD, S. 33*° E. 22.21 ch.; and DA, S. 
80^° W. 30 ch. ; it is required to divide the tract into 
two parts by a line FE, running N. 20° W. so that the 
part ABEF may be to the part FECD as 3 to 5. 

Angle A=80|°, B=123|°, C=90°, D=66°, E=76£°, 

F=79|° and P=24°. 

A . „ . ^ $E, 76° 30' Ar. Co. 0.01217 
As sin. iLXsin. t, ^ ^ 7Q 3Q 0.00733 

. A . R < A, 80 30 9.99400 

: sin. AX sin. u, J B? 12 3 30 9.92111 



AB 2 



JAB, 12 ----- 1.07918 
£AB, 12 1.07918 



fourth term 123.87 2.09297 

5 

619.35 



* The truth of this rule is evident from the demonstration to the rule in 
the last problem. 

Construction. Draw CG according to the reverse bearing of FE, and then 
proceed with the construction exactly as in the last problem. 
17* 



198 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 

A ■ Pv . F )E, 76° 30' - Ar. Co. 0.01217 

Assin. uxsin. r, j Fj 7930 _ 0.00733 

• rv • n $C, 90 00 - - - - 10.00000 

; sin.vxsin.iJ, £ d ? 66 - - - - 9.96073 

rTf X CD, 22.21 - - - - 1.34655 

• L/1 ^' I CD, 22.21 - - - - 1.34655 

: fourth term 471.33 2.67333 

3 



1413.99 
619.35 

8)2033.34 

FE=y/ 254.17= 15.94 

As sin. E, 76° 30' Ar. Co. 0.01217 

: sin. B, 123 30 9.92111 

: : AB, 12 1.07918 

: ES, 10.29 1.01246 

As sin. P, 24° 00' Ar. Co. 0.39069 

: sin. E, 76 30 9.98783 

: : FS, 5.65 0.75205 

: AF, 13.51 1.13057 

2. The boundaries of a field ABCD are given as fol- 
low : viz. AB, S. 10£° W. 7.20 ch. ; BC, S. 67° W. 12.47 
eh. : CD, N. 23° W. 13.33 ch. ; and DA, S. 89° E. 18 ch. ; 
and it is to be divided into two parts ABEF and FECD, 
in the ratio of 3 to 4, by a line FE, running due South. 
Required the length of the division line FE and the 
distance AF. Ans. FE 10.10 and AF 8.12. 



CHAP. IV.] LAYING OUT AND DIVIDING LAND. 



199 




PROBLEM XIX. 

The boundaries of a tract of 
land ABCDEFGHLA, Fig. 
108, being given, to divide 
it into tiuo equal parts by a 
line IN running from the 
corner I, and falling on the 
opposite side CD. 

RULE. 

Suppose lines drawn from I, 
to C and D, and calculate the 
area of the whole tract. 

Take the corrected latitudes and departures* of IA, 
AB, and BC, and by balancing find the latitude and 
departure of CI ; also calculate the area of the part 
IABCI ; from half the area of the whole tract, subtract 
the area of the part IABCI, the remainder will be the 
area of the triangle ICNI. 

Take the latitudes and departures of IC and CD, and 
by balancing find the latitude and departure of DI, and 
calculate the area of the triangle ICDL Then, 

As the area of the triangle ICDI, 
Is to the area of the triangle ICNI ; 
So is the latitude of CD, 
To the latitude of CN. 

Also, As the area of the triangle ICDI, 
Is to the area of the triangle ICNI ; 
So is the departure of CD, 
To the departure of CN. 



* It is the corrected latitudes and departures that are to 
throughout the calculation. 



used 



200 LAYING OUT AND DIVIDING LAND. [CHAP. IV. 

Now take the latitudes and departures of IC and CN, 
and by balancing find the latitude and departure of the 
division line NI; with which, find its bearing and 
distance.* 

EXAMPLES. 

1. Let the bearing of AB be N. 19° E. dist. 27 ch. ; BC, 
S. 77° E. 22.75 ch. ; CD, S. 27° E. 28.75 ch. ; DE, S. 52° 
W. 14.50 ch. ; EF, S. 15£° E. 19 ch. ; FG, West, 17.72 
ch.; GH, N. 36° W. 11.75 ch.; HI, North, 16.07 ch., 
and IA, N. 62° W. 14.88 ch. ; it is required to divide the 
tract into two equal parts by a line IN running from thr* 
corner I, and falling on the opposite side CD. 

First calculate the whole area, thus : 



* This rule needs no demonstration. 



.v.] 



LAYING OUT AND DIVIDING LAND. 



201 





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202 



LAYING OUT AND DIVIDING LAND. [CHAP. IV. 



To find the latitude and departure of CI, and area of the 
part IABCI. 



Sta. 


N. 


S. 


E. 


w. 


E.D.D. 


W.D.D. 


Mult. 


N. A. 


S. Areas. 


IA 


6.97 






13.13 




30.98 


0.00 E 






AB 


25.51 




8.80 






4.^3 


4.33 W 




110.4583 


BC 
CI 





5.13 


22.18 




30.98 




26.65 E 




136.7145 


(27.35) 




(17.85) 


4.33 




30.98 E 




847.3030 




32.48 


32.48 


30.98 


30.98 


35.31 


3531 






1094.4758 



Area of IABCI (sq. ch.) 547.2379 

Half area of ABCDEFGHIA 762.6990 



Area of ICNI (sq. ch.) 215.4611 



To find the area of ICDI. 



Sta. 


N. 


S. 


E. 


W. 


E.D.D. W.D.D. 1 Mult. 


N. A. 


S. Areas. 


IC 


27.35 




17.85 






13.07 1 0.00 E 






CD 




25.64 


13.07 




30.92 


30.92 E 




792.7888 


DI 




(1.71) 




(30.92) 




17.85 


13.07 E 




22.3497 




27.35 


27.35 


30.92 


30.92 


30.92 


30.92 






815.1385 



Area of ICDI (Sq. ch.) 407.5692 



As area of ICDI, 407.57 Ar. Co. 7.38980 

: area of ICNI, 215.46 2.33337 

:: latitude of CD, 25.64 S. 1.40892 



: latitude of CN, 13.55 S. - 



- 1.13209 



As area of ICDI, 407.57 Ar. Co. 7.38980 

: area of ICNI, 215.46 2.33337 

: : departure of CD, 13.07 E. 1.11628 



deoarture of CN, 6.91 E. 



- - - 0.83945 



CHAF. 1V.J LAYING OUT AND DIVIDING LAND. 



20; 



To fund tlie latitude and departure of NT. 



Sta. 


N. 


S. 


E. 


W. 


IC 


27.35 




17.85 




CN 




13.55 


6.91 




NI 




(13.80) 




(24.76) 




27.35 


27.35 


24.76 


24.76 



To find the bearing and distance of NI. 

As cliff, of lat. of NI, 13.80 S. Ar. Co. 8.86012 

: dep. do. 24.76 W. 1.39375 

: : rad. 10.00000 



: tang, bearing of NI, S. 60° 52' W. 



10.25387 



As rad. Ar. Co. 0.00000 

: sec. bearing of NI, 60° 52' 10.31261 

: : diff. lat. do. 13.80 1.13988 



: dist. NI, 28.35 ch. 1.45249 

Hence IN bears, N. 60° 52' E. dist. 28.35 ch. 



2. Given the boundaries of a tract of land as follow ; 
viz. 1st. S. 35i° W. 11.20 ch. ; 2d. N. 45° W. 24.36 ch. ; 
3d. N. 15|° E. 10.80 ch. ; 4th. S. 77° E. 16 ch. ; 5th. N. 
87i° E. 21.50 ch. ; 6th. S. 60° E. 14.80 ch. ; 7th. South, 
10.91 ch. ; 8th. N. 85° W. 29.28 ch. to the place of be- 
ginning ; to divide the tract into two equal parts by a 
line running from the first station and falling on one of 
the opposite sides ; the bearing and distance of the di- 
vision line are required. Ans. N. 7° 18' E. 15.28 ch. 



CHAPTER V. 



VARIATION OF THE COMPASS. 

A meridian indicated by the magnetic needle is not, 
in general, a true one ; for the needle does not point 
truly to the north point of the horizon, but varies from 
it, in some places to the eastward, and in others to the 
westward. 

The angle contained between the true meridian and 
that indicated by the needle, is called the variation of the 
compass. 

The variation is named east or west, according as the 
north end of the needle points to the eastward or west- 
ward of the true north. 

As the variation is different in different places, so also, 
in the same place, it does not remain the same, but 
differs sensibly in the course of a few years. Hence, 
in running a line that was run a number of years pre- 
viously, the bearing will be found different from what it 
was at that time ; this, together with some difference in 
compasses, causes many difficulties, and frequently in- 
accuracies, in tracing old lines. 



CHAP. V.] VARIATION OF THE COMPASS. 205 

The easiest way to guard against those difficulties and 
inaccuracies would be to make and return the surveys 
according to the true, and not the magnetic bearings. 
In order to do this, it will be necessary to know the va- 
riation of the compass for the place in which the survey 
is made ; and this may readily be found by first tracing 
a meridian line in the following manner. 

2 b draw a true meridian line by means of the greatest 
elongation of the pole star. 

The pole star is situated about 1£° from the true pole, 
and therefore apparently revolves round it, in a small cir- 
cle, once in about 23 h. 56 m. When at its greatest 
distance east or west from the true pole, it is said to be 
at its greatest east or west elongation. It is therefore 
evident that in the course of one apparent revolution it 
must be twice at its greatest elongation, once to the east 
and once to the west. 

The following tables exhibit the times, nearly, of the 
greatest eastern elongations of the pole star for six 
months of the year, and of the greatest western elonga- 
tions for the other six months. The other greatest elon- 
gations take place in the day time, and are therefore in- 
visible. Some of those inserted in the tables are also 
invisible ; because they occur, either before daylight is 
gone, in the evening, or after it has returned, in the 
morning. The most of those in the 3d, 4th, 9th, and 
I Oth months are in this situation. 

The time in the tables is reckoned from noon ; and 
therefore when it is less than 12 hours, the greatest elon- 
gation takes place in the evening of the same day ,• but 
when it exceeds 12 hours, if 12 hours be subtracted from 
it, the remainder will be the time of greatest elongation 

in the morning of the following day. 

18 ° J 



206 



VARIATION OF THE COMPASS. [CHAP. V. 



Eastern Elongation. 



Days. 


4 mo. (Ap.) 


5 mo 


(Ma.) 


6 mo. (Ju.) 


7 mo. (July) 


8mo.(Aug.) 


9 mo. (Sep.) 




H. M. 


H. 


M. 


H. M. 


H. M. 


H. 


M. 


H. H. 


1 


18 18 


16 


26 


14 24 


12 20 


10 


16 


8 20 


7 


17 56 


16 


3 


14 


11 55 


9 


53 


7 58 


13 


17 34 


15 


40 


13 35 


11 31 


9 


30 


7 36 


19 


17 12 


15 


17 


13 10 


11 7 


9 


8 


7 15 


25 


16 49 


14 


53 


12 45 


10 43 


8 


45 


6 53 



Western Elongations 



Days. 


10 mo 


(Oc.)llmo.(No.) 


12 mc 


.(De.) 1 mo. (Ja.) 


2 mo 


(Feb.) 


3 mo.(Mar.) 




H. 


M. 


H. 


M. 


H. 


M. 


H. M. 


II. 


M. 


H. M. 


1 


18 


18 


16 


22 


14 


19 


12 2 


9 


50 


8 1 


7 


17 


56 


15 


59 


13 


53 


11 36 


9 


26 


7 38 


13 


17 


34 


15 


35 


13 


27 


11 10 


9 


2 


7 16 


19 


17 


12 


15 


10 


13 


00 


10 44 


8 


39 


6 54 


25 


16 


49 


14 


45 


12 


34 


10 18 


8 


16 


6 33 



In order to determine a true meridian, by the method 
here used, it is necessary to know the bearing of the pole 
star, called its azimuth, at the time of its greatest elon- 
gation. This depends on the latitude of the place, and 
the distance of the star from the pole. This distance is 
called the polar distance of the star. It is subject to a 
small annual diminution, which is called its annual preces- 
sion. The polar distance of the star on the 1st. of the 
1st. month (January) 1830, was 1°35' 51"; and its annual 
precession is 19.3". 

The polar distance may be found for any subsequent 
time by multiplying 19.3", by the interval between the 
1st. of the year 1830, and the given time, and subtract- 
ing the product from 1° 35' 51". Thus, suppose the polar 



CHAP. V.] VARIATION OF THE COMPASS. 207 

distance of the pole star was required for the 1st. of the 
7th. month, (July) 1845. The interval is 15.5 years, 
and 19.3" x 15.5 gives 299.15'=:4' 59". From 1° 35' 51", 
take 4' 59 , and we have 1° 30' 52" for the polar distance 
of the star, at the time proposed.* 

When the polar distance of the pole star is known, its 
azimuth, at the time of greatest elongation may be found 
by the following proportion. 

As radius, 

Is to the secant of the latitude of the place, 

So is the sine of the polar distance, 

To the azimuth. 

This azimuth will be east or west, according as the 
elongation is east or west ; and consequently its name 
will be known from the preceding tables. 

As an example, let the azimuth of the pole star, at 
Philadelphia, latitude 39° 57', be required, for the 1st. of 
the 7th. month (July) 1845. The polar distance found 
above is 1° 30' 52"; and it may be taken 1° 31' without 
material error. 

As radius Ar. Co. 0.00000 

: secant of lat. 39° 57' 10.11543 

::sin.ofpol.dist. 1 31 8.42272 



sin. of azimuth 1° 59' E. 8.53815 



* The polar distance obtained as above, is called tbe mean polar distance ; 
and it is sufficiently accurate for our present purpose. To obtain the true 
polar distance, two small corrections called aberration and nutation, would 
have to be applied. 



208 VARIATION OF THE COMPASS. [CHAP. V. 

In order to observe the greatest elongation of the pole 
star, it will be necessary to prepare the following simple 
apparatus. 

Place two posts firmly in the ground, about three feet 
apart, and nearly east and west from each other ; the 
heights of the posts, which should be the same, may 
be about two or three feet ; on those posts, place a thick 
board or plank, five or six inches wide, and nail it fast to 
each of them, taking care that it be level or nearly so : 
take a piece of board, a foot or eighteen inches long and 
four or five wide, and near the middle of it fasten a com- 
pass-sight perpendicularly ; this board is to slide on the 
horizontal one already mentioned. 

Take a stiff pole 18 or 20 feet in length, and fix it in 
an inclined position, in such a manner that a plumb line 
suspended from the upper end, may be nearly north, 
from the middle of the horizontal board, and about ten 
feet distant from it ; the elevation of the pole must be 
such that the pole star, when viewed through the com- 
pass sight placed on the horizontal board, may appear 
a few inches below its upper end ; when in this position 
the lower end should be fastened in the ground, and the 
pole should be supported by a couple of crotchets placed 
near the middle. The plumb should weigh a pound 
or more, and should swing in a vessel of water, in 
order to prevent the line being agitated by the motion 
of the air. 

The apparatus being prepared, proceed, about 15 or 
20 minutes previous to the time of greatest elongation 
as indicated by the table, to make the observation as fol- 
lows : Let an assistant hold a lighted candle near the 



CHAP. V.j VARIATION OF THE COMPASS. SO 9 

plumb line, so as to illuminate it and render it distinctly 
visible ; place the small board with the compass- sight 
attached to it, on the horizontal one, and move it east 
or west as the case may require, till the pole star, plumb 
line, and aperture in the compass-sight are all m a direct 
range. If the star should be deviating to the east, it will 
leave the plumb-line to the west ; and the contrary, if 
deviating to the west ; keep therefore shifting the sight, 
till the star appears stationary behind the plumb-line-, 
which it will do for several minutes at the time of its 
greatest elongation, and will then recede from the line 
on the contrary side from which it did before it became 
stationary. The compass-sight must not be moved after 
the star has attained its greatest elongation ; but the ap- 
erture in it being then in a direct range with the plumb 
line and star, the board to which the sight is fixed, must 
be fastened to the one on which it slides, by a small tack 
passing through each end. This being done let an 
assistant take a straight stake, with a piece of lighted 
candle stuck on it, and go north to the distance of 30 or 
40 perches ; then looking through the compass-sight, 
direct him to set up the stake perpendicularly, and m 
such a situation that the candle stuck on the top may 
appear exactly behind the plumb-line ; when thus placed, 
let it be firmly fixed in the ground. Next, let another 
straight stake be set up in the same manner near the 
plumb-line ; the remaining part of the work may then be 
left till morning. 

Measure accurately the distance between the two 
stakes. Then, 

As radius, 

Is to the tangent of the azimuth ; 
So is the distance between the stakes, in feet, 
To a fourth term, in feet. 
2D 



210 VARIATION OF THE COMPASS. [CHAP. V. 

Lay off the distance contained in this fourth term 
from the northerly stake, and perpendicular to a line join- 
ing the two stakes ; it must be laid off towards the west 
if the azimuth is east, but towards the east if the azimuth 
is west. Next remove the northerly stake, and set it up 
at the other extremity of the distance thus laid off; then 
a straight line joining the two stakes will be a true meri- 
dian line. 

To obtain the variation, set up a compass in the place 
of the southerly stake, and direct the sights truly to the 
northerly one ; the needle will then point out the varia- 
tion, which will be east or west, according as the north 
end of the needle points to the east or west of the north 
point of the compass. The whole process is so simple, 
that an example is deemed unnecessary. 

It has already been observed, that the greatest elon- 
gations of the pole star are invisible during the greater 
part of the 3d and 4th months, and also of the 9th and 
10th; consequently a meridian line cannot be obtained 
by the preceding method, during those periods. But as 
the surveyor may generally choose his time for tracing 
a meridian line, and as, when this is done, he can at any 
time obtain the variation, it is thought unnecessary to 
introduce other methods. Those, however, who would 
wish to be acquainted with simple and accurate methods 
of tracing a meridian line at any season of the year, may 
consult a pamphlet on the subject by Andrew Elicott, A.M. 
from which the substance of the preceding method is 
extracted; and which contains others suited to those 
times of the year in which this cannot be applied. It 
may not be improper also to observe, that the second 
volume of the American Philosophical Transactions con- 



CHAP. V.] VARIATION OF THE COMPASS. 211 

tains an essay by Robert Patterson, Professor of Mathe- 
matics in the University of Pennsylvania, in which is 
given a method for obtaining the variation to a sufficient 
degree of accuracy for any purpose in surveying, and 
which has this advantage, that the observation may be 
made at any season of the year, and at any time in the 
evening. There are also other methods besides those 
alluded to above, by which a meridian line may be traced, 
or the variation of the compass determined ; but as the 
most of them require expensive instruments for making 
the observations, it is thought unnecessary to notice 
them in this work. 

To obtain the true bearings of a survey, from the magnetic 
ones, the variation being given. 

If the variation be east, add it to the north-easterly 
and south-westerly bearings, and subtract it from those 
that are north-westerly or south-easterly ; but if the 
variation be west, add it to the north-westerly and south- 
easterly bearings, and subtract it from those that are 
north-easterly or south-westerly; this being done, the 
true bearings are obtained. 

To find the difference between the present variation, and that 
at a time ivhen a tract of land ivas formerly surveyed, 
in order to trace or run out the original lines. 

Go to any part of the .premises, where any two adja- 
cent corners are known ; and if one can be seen from the 
other, take its bearing ; which compared with that of 
the same line in the former survey, shows their differ- 
ence. But if one corner cannot be seen from the other, 
run the line according to the given bearing, and measure 



212 VARIATION OF THE COMPASS. [CHAP. V. 

the nearest distance between the line so run, and ths 
corner ; then, 

As the length of the given line, 

Is to the said distance ; 

So is 57.3 degrees.* 

To the difference of variation required. 

EXAMPLE. 

Suppose it be required to run a line, which some years 
ago bore N. 45° E. dist. 20 ch. and in running this line 
by the given bearing, the corner is found 20 links to the 
left hand ; what allowance must be made on each bear- 
ing to trace the old lines ; and what is the present bear- 
ing, by the compass, of this particular line ? 



L. 


L. 


Deg. 


As 2000 


: 20 


: : 57.3 
20 



2000)1146.0(0° 34' 

Consequently 34 minutes, or a little more than half a 
degree, is the allowance required ,; and the line in ques- 
tion bears N. 44° 26' E. 



Note. The above rule is simple and sufficiently ac- 
curate when the distance between the sought corner and 



* 57.3 is the radius (nearly) of a circle in such parts as the circumference 
contains 360- 



CHAP. V.] VARIATION OF THE COMPASS 213 

random line, is small. But when this distance is con- 
siderable, it will be better to find the angle by trigono. 
metry. 



ON LOCAL ATTRACTION. 

It is well known that iron or any ferruginous substance 
attracts the magnetic needle, and consequently when near, 
will draw it aside from the position in which it would 
otherwise settle. And as the earth in many places con- 
tains, near its surface, substances of this kind, the needle 
will not unfrequently be attracted from its true direction. 
The surveyor ought therefore, at each station, to take a 
back sight to the preceding one j and if he arrive at one 
at which the compass does not reverse truly, he may 
conclude, provided no error was committed in taking the 
bearing at the last station, that at the present one, the 
needle is affected by some local attraction. In such a 
case, he should first determine whether any error was 
committed at the last station, and if none is found, take 
the difference between the bearing from the last station 
and the reverse bearing, which will be the local variation 
of the needle at the present station. This variation musi 
be applied, according to its name, to the bearing of the 
following station. 

If at the first and second station of a survey the com- 
pass is found not to reverse truly, the surveyor will be at 
loss to know which of them is affected by attraction. 
But by taking another station, either within or without 
the survey, and taking its bearing from each of those 



214 VARIATION OF THE COMPASS. [CHAP. T. 

stations, and the bearing of each of those from it, he may, 
in general, determine at which of them the attraction 
exists. 

Note. — The area of the survey is not affected by the 
general variation, because it is the same at each station. 
But where local attraction exists and causes a variation 
in the position of the needle, as this variation will be dif- 
ferent at different stations, it will, unless ascertained, and 
allowed on the corresponding bearings, materially affect 
the truth of the survey. 



CHAPTER VI. 



MISCELLANEOUS QUESTIONS. 

1. A circular fish-pond is to be dug in a garden, that 
shall take up just half an acre : what must be the length 
of the cord that strikes the circle ? 

Arts. 27.75 yards. 

2. Two sides of a triangle are 20 and 40 perches re- 
spectively : required the third side, so that the content 
may be just an acre. 

Ans, Either 23.099 or 58.876 perches. 

3. In 110 acres of statute measure, in which the pole 
is 5.5 yards, how many Cheshire acres, where the cus- 
tomary pole is 6 yards ; and how many of Ireland, where 
the pole in use is 7 yards ? 

Ans. 92 A. 1 R. 29 P. Cheshire ; 67 A. 3 R. 25 P. Irish. 

4. The ellipse in Grosvenor square, London, measures 
840 links the longer way, and 612 the shorter, within 
the rails ; now the wall being 14 inches thick, it is requi- 
red to find what quantity of ground it encloses, and how 
much it stands upon. 

Ans. It encloses 4 A. OR. 6 P. and stands on 1760| 
square feet 

5. Required the dimensions of an elliptical acre, with 
the greater and less diameters in the ratio of 3 to 2. 

Ans. 17.481 by 11.654 perches. 



216 MISCELLANEOUS QUESTIONS. [CHAP. VI. 

6. The three sides of a triangular field, containing 
6 A. 1 R. 12 P. are in the ratio of the three numbers, 9, 
8, 6, respectively ; required the sides. 

Ans. 59.029, 52.47, and 39.353 perches. 

7. In a pentangular field, beginning with the south 
side and measuring round towards the east, the first or 
south side is 27.35 ch., the second 31.15 ch., the third 
23.70 ch., the fourth 29.25 ch., and the fifth 22.20 ch. ; 
also the diagonal from the first angle to the third is 38 
eh., and that from the third to the 5th. 40.10 ch.; required 
the area of the field. Ans. 117 A. 2 R. 39 P. 

8. Required the dimensions of an oblong garden, con- 
taining three acres, and bounded by 104 perches of pale 
fence.* Ans. 40 P. by 12. 

9. How many acres are contained in a square mea- 
dow, the diagonal of which is 20 perches longer than 
either of its sides 1 Ans. 14 A. 2 R. IIP. 

10. A gentleman has a garden 100 feet long and 80 
broad, and a gravel walk is to be made of equal width 
half round it; what must be the width of the walk, so that 
it may take up just one fourth of the ground. 

Ans. 11.8975 feet. 

11. A person has a circular yard that is 150 feet in 
diameter, and wishes a walk of equal width made round 
it within the fence: required the width of the walk so that 
it may occupy a fifth part of the ground. 

Ans. 7.918 feet. 



* This question may be neatly constructed by 28, 6 Playf air's Geometry. 
It may not be improper also to observe, that the 2d question, and all those 
following the 8th, admit of neat geometrical constructions. 



CHAP. VI.] MISCELLANEOUS QUESTIONS. 217 

12. From a point within a triangular field the sides 
of which were equal, I measured the distances to the 
three angles, and found them 12.5, 10, and 7.5 chains, re- 
spectively ; required the area. Ans. 12 A. 1 R 23 P. 

13. On examining the field-notes of a lot of ground of 
which I wished to know the content, I found them as fol- 
low : 1st, S. 72° W. 24 per., 2d. North, 38 per., 3d. N. 

82£ E. 41 per., 4th. , 20 per., 5th. S. 80° E. 11.5 per., 

6th. S. 26° W. 22 per., and 7th. , 37 per., to the place 

of beginning. The bearings of the 4th and 7th bounda- 
ry lines were illegible ; but the data remaining being suf- 
ficient, the area is required. 

Ans. 12 A. 3 R. 2 P. 

14. It is required to lay out 4$ acres of land in a tri- 
angular form, so that the length of one side may be 15 
chains, and the lengths of the other sides in the ratio of 
2 to 3 ; what must be the lengths of those sides ? 

Ans, 7.7914 and 11.6871 chains; or 29.58536 and 
44.37804 chains. 

15. It is required to lay out five acres of ground in a 
triangular form to be bounded by 135 perches of fence ; 
the length of one side is to be 50 perches ; what must be 
the lengths of the other sides ? 

Ans. 33.3785 and 51.6215 perches. 

16. The area of a rectangular field is 7£ acres and the 
length of the diagonal 50 perches : required the sides. 

Ans. 30 and 40 perches. 

17. In a rectangular tract of land, containing 58 A. 3R. 

8 P. the difference of the lengths of the sides is just, equal 

to the difference between the lengths of the longer side 

and the diagonal ; hence the sides are required. 

Ans. 21 and 28 chains. 
19 2E 



218 MISCELLANEOUS QUESTIONS. [cHAP. VI. 

18. The boundaries of a tract of land are as follow : 
1st. N. 14° W. 15.20 ch. ; 2d. N. 70£° E. 20.43 ch. ; 3d. 
S. 6° E. 22.79 ch. ; 4th. N. 86£° W. 18 to the place of 
beginning ; within the tract there is a spring, the bearing 
and distance of which, from the 2d corner, is S. 75° E. 
7.90 ch. It is required to cut off 10 acres from the west 
side of this tract by a straight line running through the 
spring ; what must be the distance of the division line 
from the 1st corner, measured on the fourth side. 

Ans. 4.6357 chains. 

19. The boundaries of a quadrilateral tract of land are 
as follow : 1st. N. 35i° E. 23 ch. ; 2d. N. 75£° E. 30.50 
ch. ; 3d. S. 3F E. 46.49 ch. and 4th. N. 661° W. 49.64 ch., 
to the place of beginning. This tract is to be divided 
into four equal parts by two straight lines, one of which 
is to run parallel to the 3d side ; required the distance 
of the parallel division line from the first corner, measur- 
ed on the 4th side ', also the bearing of the other division 
line, and its distance from the same corner, measured on 
the first side. 

Ans. Distance of the parallel division from the first 
corner 32.50 chains ; the bearing of the other, S. 88° 22* 
E. and its distance from the same corner 5.99 chains. 



CHAPTER VII. 



OF THE THEODOLITE. 

A Vertical Angle is any angle in a plane perpen- 
dicular to the horizon. Consequently angles of eleva- 
tion and depression are vertical angles. 

A Theodolite is an instrument used to measure both 
horizontal and vertical angles. 

By the aid of a theodolite, surveys may be much 
more accurately made than with the compass, espe- 
cially when the tract is large or the ground hilly, or 
where there is local attraction. Before describing the 
theodolite, it will be best to notice separately one or 
two of its appendages. 

Of the Spirit Level. 

The Spirit Level consists principally of a cylindrical 
glass tube, nearly, but not entirely, filled with alcohol, 
or some other fluid. The inner part of that side of 
the tube which, when in use, is to be uppermost, is 
ground from end to end into a regular curve, having 
its convexity upwards. In consequence of this curva- 
ture in the upper part of the cavity, the air bubble, or 
part not occupied by the fluid, must be at the middle 
of the tube when the axis of the level, that is, the 
straight line passing lengthwise through its middle, is 
in a horizontal position. And conversely the axis 
must be horizontal when the instrument is so placed 
that the bubble stands at the middle of the tube. 



220 OF THE THEODOLITE. [CHAP. VI». 

Of the Vernier. 

A Vernier is a graduated index which serves to sub- 
divide the smallest divisions of a graduated arc or 
straight line. 

Verniers are somewhat different according to the 
value of the divisions which they are to subdivide and 
the degree of precision they are designed to give ; but 
the principle of construction is the same in all. The 
following description applies to the vernier attached to 
the common theodolite, the limb of which is divided 
into degrees and half degrees, numbered from 0° to 
360°; and the vernier subdivides the half degrees to 
minutes. 

In Fig. 115, AB represents a part of the graduated 
limb, and CD the vernier ; the whole being drawn on 
an enlarged scale. The extent of the vernier is ex- 
actly equal to 29 half degrees, or 870 minutes, on the 
limb, and is divided into 30 equal parts, numbered from 
to 30. Each division of the vernier contains there- 
fore 29 minutes. Hence it is evident that when the 0, 
or zero line of the vernier exactly coincides, as in the 
figure, with a division line on the limb, the first divi- 
sion line of the vernier must be one minute behind the 
line on the limb first following that with which the zero 
of the vernier coincides ; the second line of the ver- 
nier must be two minutes behind the second on the 
limb; the third line on the vernier must be three 
minutes behind the third on the limb; and so on. If 
then, the vernier were to be moved forward till its first 
division line coincided with the first on the limb, the 
zero of the vernier would be one minute past the line 
on the limb with which it before coincided ; if moved 
till the second lines coincided, the zero of the vernier 



CHAP. VII.J OF THE THEODOLITE. 221 

would be two minutes past the same line ; and in like 
manner for other coincidences. It therefore follows 
that for any position of the vernier, the number of the 
division line on it which coincides with one on the limb, 
must express the number of minutes that the zero of 
the vernier is past the division line on the limb, next 
preceding it. 

The arc indicated by the vernier index in any posi- 
tion is the arc intercepted in the direction in which 
the degrees are numbered between the zero line of the 
limb and the zero line of the vernier. Hence to find 
the arc, or as it is technically expressed, to read off 'the 
arc, we must add to the arc expressed by the number 
of whole degrees intercepted and the odd half degree, 
if there is one, the number of minutes indicated by the 
number of that division line on the vernier which coin- 
cides, or is the nearest to coincidence, with one on the 
limb. Thus, as the zero of the vernier in Fig. 115 
exactly coincides with the division line on the limb, 
numbered 50, the arc indicated is 50°. In Fig. 116, 
the zero of the vernier is past the line on the limb de- 
noting 52° 30', and the 21st division line of the ver- 
nier coincides with a line on the limb. The arc indi- 
cated is therefore 52° 51'. 

Sometimes it is requisite that the vernier should 
serve to read off an arc on either side of the zero line 
In this case the zero of the vernier is placed at its mid- 
dle, and the division lines have two sets of numbers, 
as in Fig. 117. The upper numbers are used when the 
zero of the vernier is to the right of the zero of the 
arc, and the lower ones when it is to the left. The arc 
indicated by the vernier in the position that it has in 
the figure, is 2° 12' to the right. 

To determine the reading of a vernier, applied to a 
19 * 



222 OF THE THEODOLITE. [CHAP. VII. 

graduated arc in which the value of the least division is 
more or less than half a degree, we must divide this 
value by the number of divisions on the vernier, and 
the quotient will indicate the reading that the vernier 
is intended to give. In the nautical instrument called 
a sextant, the value of the least division on the limb is 
usually 10 minutes, and the vernier is divided into 60 
equal parts. Hence 10 minutes, or 600 seconds, di- 
vided by 60, gives 10 seconds for the reading of the 
vernier. 

Description of the Theodolite. 

The Theodolite is represented in Fig. 109. When 
in use, the lower circular plate AB is screwed fast to a 
three-legged stand or tripod, the upper part of which 
is represented in the figure. The circular plate CD 
has a hollow axis passing through it at right angles at 
its centre, and firmly attached to it. The lower part 
of the axis terminates in a ball, to which it is fastened 
by a screw. This ball is partly enclosed in a socket 
projecting from the upper side of the plate AB ; the 
opening in the upper part of the socket being larger 
than the axis, so as to allow the latter some motion in 
every direction. In the lower plate AB, four screws 
called levelling screws, are inserted, standing opposite 
each other in pairs, the tops of which press against 
the under side of the plate CD. These screws are 
turned by milled projections or heads, two of which 
are shown in the figure. By turning them in opposite 
directions, the position of the plate CD may be changed 
so that it may be made level, even when the lower 
plate AB has considerable inclination. 

The part GH of the instrument consists of two cir- 
cular plates in close contact with each other. The 



\ 

CHAP, VII. J OF THE THEODOLITE. 223 

lower one is called the graduated plate, and its cham- 
fered edge, which is usually made of silver, is called 
the limb of the instrument. To the central part of 
this plate, a hollow axis is attached, the cavity of 
which fits to the outside of the axis of the plate CD, 
so that the former may move easily and steadily about 
the latter. The lower part of the axis is embraced by 
a clamping-piece that may be tightened or loosened by 
the screw E. When the clamp is loose, the graduated 
plate may be turned round by the hand ; but when it is 
made fast, the axis of the graduated plate, and conse- 
quently the plate itself, becomes firmly connected with 
the plate CD, and also, when the levelling screws are 
tight, with the stand of the instrument. The gradu- 
ated plate may however, when thus connected, be 
moved a small distance either way by turning the screw 
F, called a tangent-screw, which gives it a slow motion. 
Around the axis of the graduated plate is another hol- 
low axis, with which a telescope, called the lower tele- 
scope, is connected. When the axis of the graduated 
plate is clamped fast, this axis and the telescope may 
be made to revolve by turning the milled head I, and 
may be secured in any position by the screw K, which 
clamps the axis to the graduated plate. 

The plate immediately above the graduated plate is 
called the vernier plate. It has, at its centre, a solid 
axis which fits into the cavities of the hollow axes of 
both the graduated plate and plate CD. When the 
screw L, which serves to clamp the vernier plate to 
the graduated plate, is loosened, the former may be 
turned round by hand ; and when this screw is made 
tighi, a slow motion may be given to the vernier plate 
by the tangent-screw M, The vernier plate has tfro, 
or sometimes three, verniers at different parts of its 



224 OF THE THEODOLITE. [CHAP. VII. 

edge, which are chamfered for the purpose. When 
there are only two, they are placed directly opposite 
to each other. When there are three, they are placed 
at equal distances around the edge. The microscope 
S is used to enable the eye more certainly to distin- 
guish the line on the vernier that coincides with one 
on the limb. Two levels are placed on the vernier 
plate, at right angles to each other ; one of which is 
shown in the figure. 

The frame which supports the vertical semicircle 
and upper telescope with its attached level, is attached 
to the vernier plate by three screws at equal distances 
from one another. The immediate supports of this 
telescope are called wyes, or Y's, from their resem- 
blance to the letter Y. The telescope is held in its 
place by two curved pieces, moveable on joints, which 
pass over it and are fastened by the pins T and U. 
When these pins are taken out, the pieces may be 
turned back and the telescope taken from its place and 
reversed, that is changed end for end. 

In the tube of the telescope a flat ring is placed at 
right angles to its axis, and connected with the tube by 
four screws, opposite to each other in pairs ; the heads 
of three of which, b, c, and d, are shown. Two spi- 
der's lines or very fine wires, at right angles to each 
other, are attached to the ring, in the directions re- 
spectively of each pair of screws, and intersecting 
each other in the centre of the ring. At each end of 
the principal tube, and fitting it on the inside, a short 
moveable tube is inserted. The one at the end to 
which the eye is applied, and which usually contains 
several glass lenses, may be moved out or in, by a 
small pin attached to its lower side, and may thus be 
so adjusted as to render the spider's lines distinctly 



CHAP. VII.] OF THE THEODOLITE. 225 

visible. The tube at the other end, which contains 
one lens, may be moved out or in, by turning the milled 
head V, and may be thus so placed as to render an 
object to which the telescope is directed, as distinct as 
its distance permits. 

A straight line in the direction in which the inter- 
section of the spider's lines or wires is seen by an eye 
placed at the eye end of the telescope, is the line of 
sight of the telescope, and is technically called the 
line of collimation. The telescope is said to be directed 
to any point in an object, when it is so placed that the 
line of collimation passes through the point ; or which 
is the same, when the point is directly behind the in- 
tersection of the spider's lines. 

The semicircle PQ is called the vertical limb of the 
instrument. That face of it which is not seen in the 
figure is divided into degrees and half degrees, num- 
bered each way from a line taken as a zero or line ; 
and the arc is read by a vernier numbered as in Fig. 
117. The other face has two sets of unequal divi- 
sions on it, numbered each way from a zero line. One 
of these denotes the difference between the real dis- 
tance of an object to which the upper telescope is di- 
rected and its horizontal distance, expressed in 100th 
parts of the distance. The other denotes the vertical 
distance of the object, above or below a horizontal 
line, passing through the instrument, expressed in 100th 
parts of the horizontal distance. The vertical limb is 
moved so as to give to the telescope different inclina- 
tions to the horizon, by means of the milled head N. 

At the bottom of the frame which supports the ver- 
tical limb and upper telescope, and directly over the 
centre of the vernier plate, there is a compass box, 

containing a magnetic needle. This part of the 
, 2 F 



226 OF THE THEODOLITE. [CHAP. VIT 

instrument may be used to take the bearing of an 
object in the same manner as a common compass. 

ADJUSTMENTS OF THE THEODOLITE. 

In order that the theodolite may be in a good state 
for use, the line of collimation of the upper telescope 
should exactly coincide with the axis of the telescope : 
the axis of the attached level should be parallel to this 
line ; the axes of the levels on the vernier plate should 
be parallel to this plate ; the line of collimation of the 
telescope should, when the milled head N is turned, 
move in a plane perpendicular to the vernier plate : 
and when this line is brought parallel to the vernier 
plate, the zero of the vertical limb should coincide with 
the zero of its vernier. Previous therefore to using 
the instrument, the different parts should be examined, 
and adjusted if necessary. This may be done by the 
following methods. 

FIRST ADJUSTMENT. 

To make the line of collimation coincide with the axis of 
the telescope. 

The instrument being firmly screwed on the tripod 
and the legs of the latter being sufficiently extended to 
ensure its remaining fixed in its position, loosen the 
clamp screw L, and turn the vernier plate till the tele- 
scope points to some distant object having on it a 
small well-defined point. Then, having fastened the 
screw L, move the telescope by the tangent-screw M, 
and milled head N, till the line of collimation is di- 
rected exactly to the point. 

Revolve now the telescope in its Y's, half round, 
that is, till the level, from being directly below the tele- 



CHAP. VII.] OF THE THEODOLITE. 227 

scope is directly above it. If the horizontal spider's 
line still coincides with the point, it requires no adjust- 
ment ; but if it does not, diminish the distance one- 
half, by loosening one of the screws c and d and tight- 
ening the other; and then bring the line to coincide 
with the point by means of the milled head N. Re- 
volve the telescope round to its first position, and if 
the horizontal line and point do not then coincide, 
repeat the operation till the coincidence has place in 
both positions. In a similar manner the vertical line 
may be adjusted. When both adjustments are com- 
plete, the line of collimation should coincide with the 
same point during a complete revolution of the tele- 
scope in its Y's. 

SECOND ADJUSTMENT. 

To make the axis of the level attached to the upper tele- 
scope parallel to the line of collimation. 

Turn the vernier plate till the telescope comes di- 
rectly over two of the levelling screws ; and if the 
telescope is not nearly in a horizontal position, make 
it so by turning the milled head N. Then turn the 
levelling screws over which the telescope stands, in 
opposite directions, till the bubble of the level stands 
exactly at the middle of the tube ; observing to keep 
the screws firm against the plate CD. When this is 
done, reverse the telescope in its Y's, and if the bubble 
does not stand at the middle of the tube, correct half 
of the deviation by one of the screws m and n, which 
serve to raise or depress the ends of the level, and 
then, by the levelling screws, bring the bubble to the 
middle. Again reverse the telescope and repeat the 
correction if necessary. 



228 OF THE THEODOLITE [CHAP. VII. 

Revolve now the telescope in its Y's so as to bring 
the level a considerable distance from its proper or 
lowest position, and if the bubble deviates from the 
middle of the tube, make the requisite correction by 
means of two screws, p and y, which move the end of 
the level laterally, one of which is shown at p. When 
this part of the adjustment has been so made that the 
bubble will remain in the middle of the tube while the 
telescope is revolved either way, the first part of the 
adjustment should, by again reversing the telescope, 
be examined, and repeated if necessary. 

THIRD ADJUSTMENT. 

To make the axes of the levels on the vernier plate paral- 
lel to that plate. 

Turn the vernier plate till the upper telescope stands 
over two of the levelling screws ; then one of the 
levels on this plate will be parallel to these two screws, 
and the other will be parallel to the other two. By 
means of these levelling screws bring the bubbles of 
both levels to stand in the middles of their respective 
tubes. Then move the vernier plate 180°, and if the 
bubble in either of the levels deviates from the middle, 
correct one-half of the deviation by one of the screws 
at its ends, and the other half by the levelling screws, 
parallel to it ; and if the bubble of the other level also 
deviates from the middle, proceed in the same way to 
correct the deviation. Repeat the operations till the 
bubbles of both levels will remain at the middles of 
their respective tubes during a complete revolution of 
the vernier plate. 



CHAP. VII.] OF THE THEODOLITE. 229 

FOURTH ADJUSTMENT. 

To make the axis about which the vertical limb revolves, 
parallel to the vernier plate. 

Turn the vernier plate till the upper telescope is 
directed towards a well-defined, elevated point, on a 
house or other object, not very remote, and having 
clamped the plate, direct the telescope by means of the 
tangent-screw M and milled head N, exactly to the 
point. Then turn the milled head N till the line of 
collimation coincides with some well-defined point 
near the ground ; or, if none such is found, let an 
assistant make a suitable mark in the direction of the 
line of collimation when thus brought nearly horizon- 
tal. This being done, reverse the telescope in its Y's ; 
and, proceeding as before, direct it to the elevated 
point. Then, if by turning the milled head N, the line 
of collimation is brought to coincide with the lower 
point or mark, the axis of the vertical limb is parallel 
to the vernier plate ; but if this is not the case, the 
adjustment must be made by the screws which attach 
the upper frame to this plate. 

FIFTH ADJUSTMENT. 

To adjust the vernier of the vertical limb, or determine 
the correction which should be made, to allow for its 
deviation from correct adjustment. 

Direct the upper telescope to some elevated point 
and note the angle of elevation indicated by the ver- 
nier. Reverse the telescope in its Y's, and again direct 
it to the same point, and note the angle of elevation. 
If the angles are the same, the vernier is properly 
20 



230 OF THE THEODOLITE. [CHAP. VII. 

adjusted. If they differ, the position of the vernier 
requires adjustment ; and this may be effected by the 
screw v, which is one of those that fasten the upper 
frame to the vernier plate. 

Instead of changing the position of the vernier, we 
may take half the difference of the two angles of ele- 
vation as a correction, to be added to all those angles 
of elevation and subtracted from those of depression, 
that are taken with the telescope in that position in 
its Y's, which gave the least of the two angles ; but 
to be applied in a reverse manner when the position 
of the telescope is that which gave the greater angle 

SIXTH ADJUSTMENT. 

To make the axis about which the lower telescope revolves 
vertically, perpendicular to the axis of the instrument. 

Turn the vernier plate till the levels on it are re- 
spectively parallel to a pair of opposite levelling screws, 
and by means of these screws bring the bubbles to 
stand in the middles of the tubes; the instrument is 
then levelled, and its axis is perpendicular to the hori- 
zon. Suspend a plumb-line of considerable length at 
a short distance from the instrument, and loosening 
the clamping screw K, turn the milled head I, till the 
telescope is directed to the line, and then fasten the 
clamping-screw. Now, applying the hand to the eye- 
end of the telescope, move it vertically, and observe 
whether it continues directed to the line, throughout 
its whole extent. If it does, the axis is properly ad- 
justed; if it does not, the adjustment may be made 
by two small screws which move the remote end of 
the axis vertically. 

The lower telescope being used only as a guard to 



CHAP. VII.] OF THE THEODOLITE. 231 

ascertain whether or not the horizontal limb of the 
instrument remains fixed while the vernier plate is 
made to revolve, in order to direct the upper telescope 
to an object, requires no other adjustment than the 
above, except those for distinct vision of the spider's 
lines and object.* 

In extensive practical operations, the above adjust- 
ments should be examined, and corrected if necessary, 
not only before the commencement, but every day or 
two during their continuance. 



*& 



Of the arc of the horizontal limb, corresponding w a 
given position of the vernier plate. 

When there is but one vernier, the arc indicated by 
it is regarded as the corresponding arc. When there 
are two or three, it is usual to distinguish them by 
calling one A, another B, and the third, if there is a 
third, C, and to consider the arc indicated by the ver- 

* When the foregoing adjustments have been completed for the first time, 
there is another examination which it is well to make. Direct the upper 
telescope to some well-defined point near the horizon, and note the arcs on 
the horizontal limb, indicated by the different verniers. Then having di- 
rected the lower telescope to the same point, fasten its clamping-screw K ; 
examining first, however, to see that the upper telescope has not changed 
its position, or if it has, bringing it back by the tangent-screw F. Reverse 
now the upper telescope in its Y's, and again direct it to the point; exa- 
mining at the same time to see that the lower telescope has not changed its 
position, or, if it has, bringing it back by the tangent-screw F. Note the 
arcs indicated by each of the verniers ; and subtract the arc indicated by 
each verniei in the former position from that in the latter, increasing that of 
the latter by 360°, if necessary. Add together the remainders, and divide 
the sum by the number of verniers. If the quotient is 180°, we infer that 
the axis about which the upper telescope revolves is, as it ought to be, at 
right angles to the line of collimation of the telescope. If the quotient dif- 
fers materially from 180°, the instrument is imperfect, except one of the Y's 
is laterally adjustable. Where this is not the case, the imperfection can 
only be well remedied by an instrument-maker. If the remainders men- 
tioned above differ much from each other, we infer that the instrument has 
cot been well centered, or not well divided. 



232 OF THE THEODOLITE [CHAP. VII. 

nier A, as expressing the position of the vernier plate, 
at least very nearly ; the readings of the other ver- 
niers being used merely as a test, or means of cor- 
recting the former. We therefore note the arc indi- 
cated by the vernier A. Then note the minutes of the 
arc indicated by the vernier B ; but instead of the 
number of degrees indicated by it, we take either the 
number indicated by the vernier A, or this number in- 
creased or diminished by a unit, so that the arc set 
down for the vernier B, may be very nearly the same 
as that for the vernier A. If there is a third vernier 
C, we proceed in the same manner. Then the sum of 
the arcs obtained for each vernier, divided by the num- 
ber of verniers,* will give the value of the arc corre- 
sponding to the given position of the vernier plate, or, 
as it is sometimes expressed, the arc indicated by the 
verniers. Thus, if we suppose the instrument to have 
three verniers, and that for a given position of the 
plate, the reading of the vernier A is 142° 2', of B, 
261° 58', and of C, 22° 3' ; then, instead of these quan- 
tities for B and C, we write for B, 141° 58', and for C, 
142° 3'. Adding together 142° 2', 141° 58', and 142° 3', 
and dividing the sum by 3, we obtain 142° 1', for tho 
arc indicated by the verniers. 

PROBLEM I. 

To measure with the Theodolite the horizontal angular 
distance of two objects, as seen from a given station. 

By means of a plumb-line suspended from the centre 
of the plate which forms the top of the tripod, set the 

* When, as is commonly the case, the number of the degrees of the arc 
for each vernier is the same, we need only divide the sum of the minutes 
of the arcs, by the number of verniers, and annex the quotient to that num- 
ber of degrees. 



CHAP. VII.] OF THE THEODOLITE. 233 

centre of the instrument directly over the station- 
mark, and then level it, as directed in the sixth adjust- 
ment. Direct the upper telescope to the object which 
stands to the left, when the face is turned towards the 
angle to be measured, and note the readings of the 
verniers. Then, having directed the lower telescope 
to the same object and fastened its clamping-screw K, 
direct the upper telescope to the other object, and note 
the readings of the verniers ; observing first however, 
whether there has been any change in the position of 
the lower telescope ; and if there has, bringing it back 
to the object at the left by means of the tangent-screw 
F, and again by the tangent-screw M, adjusting the 
direction of the upper telescope to the object at the 
right. Subtract the arc which expresses the first posi- 
tion of the vernier plate, found from the readings of 
the verniers, from that which expresses the second po- 
sition, found in like manner, increasing the latter by 
360°, if necessary, and the remainder will be the angle 
required.* 

* Sometimes, in order to give greater precision to the result, the operation 
is repeated two or three or more times. When this is done, the verniers 
need only he read at the first and last positions of the vernier plate. The 
method of proceeding is as follows : After the upper telescope has heen 
directed to the object at the right, loosen the clamping-screw E, and turn 
the instrument round till the upper telescope points towards the object at the 
eft, then fasten the screw, and by means of the tangent-screw F, direct the 
telescope accurately to the object. Then, having directed the lower tele- 
scope to this object, and fastened its clamping-screw, direct the upper tele- 
scope again to the object at the right, in the usual way. The vernier plate 
must then have moved, from its first position, a distance equal to twice the 
measure of the angular distance of the objects. If the operation be again 
repeated, the distance moved by the plate must be equal to three times the 
measure of the angle ; and so on. Hence, if the arc which expresses the 
first position of the vernier plate be subtracted from that which expresses its 
last position, and the remainder, or, when the plate has made more than a 
complete revolution, the remainder increased by 360°, be divided by the 
number which denotes the number of times the operation has been per- 
formed, the quotient will be the angle required. 
20 * 2 G 



234 OF THE THEODOLITE. [CHAP. VII. 

PROBLEM II. 

To measure a vertical angle with the Theodolite. 

The instrument being placed and levelled, direct the 
upper telescope to the point, of which the angle of ele- 
vation or depression is to be taken. Then, if the ver- 
nier of the vertical limb is accurately adjusted, the 
angle indicated by it will be the angle required. When 
this is not known to be the case, after having noted 
the arc indicated by the vernier, move the vertical 
limb till the telescope is horizontal, as indicated by the 
bubble of its level standing in the middle of the tube, 
and note the arc then indicated by the vernier. If in 
both positions the zero of the limb is on the same side 
as the zero of the vernier, subtract one arc from the 
other ; but if on different sides, add the two arcs toge- 
ther. The result will be the required angle. 

PROBLEM III. 

To measure with the Theodolite, the angles of a tract of 
land, as ABCDEFGHA, Fig. 110; and having these 
and the measures of the sides, to find the content. 

Set up the instrument at one of the angles as A, and 
also set up sight poles at H and B, or at some distant 
points in the sides AH and AB, and then measure the 
angle as directed in Prob. I. Proceed in the same way 
to measure the other angles of the tract, observing 
that the angle H, which is called a re-en&am angle, is 
to be regarded as measured by the arc aoc, and is 
therefore greater than 180°. 

When there are fences or other obstructions along 
the sides, the instrument must be set up at some dis- 
tance from the corner, and the poles must be placed 



CHAP. VII.] OP THE THEODOLITE. 235 

respectively as far from each side as the instrument is 
from the range of that side, so that straight lines from 
the instrument to the poles, may be parallel to the sides. 

With the theodolite, or, which is better, with a com- 
pass, take the bearing of one of the sides, as AH. 
With this bearing and the angle A, find the bearing 
of AB. Then with the bearing of BA, which is the 
reverse of the bearing of AB, and the angle B, find the 
bearing of BC ; and proceed thus, to find the bearings 
of the other sides. 

Having measured the horizontal lengths of the sides, 
and obtained the bearings from the measured angles, 
the content may be found by prob. 12, chap. III.; ob- 
serving that as the differences of latitude and the de- 
partures are given in the traverse table, only for every 
quarter of a degree, they should be computed for each 
side by prob. 10, chap. I. ; or, if they are taken from 
the traverse table, proportional parts should be applied 
for the odd minutes, above full quarters of a degree. 

Note 1. When the angles of the tract have all been 
measured, the accuracy of the measures may be tested 
as follows. Subtract 2 from the number of sides of 
the tract, and multiply 180° by the remainder; the 
product will express the sum of all the interior angles 
(32. 3. cor. 1.) Hence if the sum of the measured 
angles is equal, or very nearly equal, to this sum, they 
may be regarded as having been correctly taken ; but 
should the sums differ considerably, an error in one or 
more of the angles must have been committed, and the 
operations should be repeated. 

2. In measuring the lengths of the sides, if any of 
them have a considerable ascent or descent, and if 



236 OF THE THEODOLITE. [cHAP. VII. 

this ascent or descent is tolerably regular, it will be 
more convenient to measure their real lengths along 
the ground, and then by the theodolite determine for 
each of them the quantity that must be subtracted in 
order to obtain the horizontal lengths. To do this, 
let a mark be made on the pole at the farther end of 
the line, at the same height from the ground as the 
axis of the vertical limb of the theodolite, and diiect 
the upper telescope to this mark. The index to that 
arc of the vertical limb, which is graduated for the 
purpose, will then indicate the number of links which 
must be subtracted from each chain in the measured 
length, to obtain the horizontal length. 

3. Instead of measuring all the sides and angles, we 
may take two or three or more stations within the 
tract, and apply the method given in the 13th problem 
of chap. III. The stations should be so chosen that 
none of the angles contained between the lines which 
connect any two of the stations with a corner of the 
tract, should be either very acute or very obtuse. 
When the stations are judiciously chosen, their hori- 
zontal distances accurately measured, and the requi- 
site angles, contained between the lines joining the 
stations with one another and with the corners of the 
tract, are carefully taken with a good theodolite, the 
content may in this way be very correctly determined. 
We may also, if it is required, compute the sides and 
angles of the tract; and thence, if the bearing of one 
of the sides or of one of the lines joining a station 
with a corner, has been taken, the bearings of all the 
sides may be obtained. 



CHAP. VII.] OF THE THEODOLITE. 237 



PROBLExM IV. 

To run a line with the Theodolite from one end B, of a 
given line AB, Fig. 118, that shall make a given angle 
with that line. 

Let the theodolite be placed at B and levelled. 
Then, a sight-pole being set up at A, direct the tele- 
scopes to it and note the arc indicated by the verniers. 
Add the given angle to this arc, and turn the vernier 
plate till the arc indicated by its verniers is equal to 
the sum, and clamp it in that position. Look through 
the lower telescope to ascertain whether the graduated 
plate has changed its position, and if it has, bring it 
back by the tangent-screw F. If the upper telescope 
is not nearly parallel with the ground in the direction 
in which it points, make it so, by turning the milled 
head N, and then let a sight-pole be set up at some 
distant point exactly in the direction of the line of col- 
limation. Suppose C to be such a point. Then will 
BC be the required lino. This line may be, if desired, 
marked by driving a number of stakes into the ground 
at convenient distances along it, using the telescope to 
have them accurately placed. 

Tf it is required to extend the line beyond the point 
C, let a sight-pole be set up at B, and the theodolite be 
removed to C. Then proceed to set up a pole at an- 
other point D, exactly as directed above, except that 
the given angle must now be considered as being 180°, 
in order that CD may be in the same direction with 
BC. Or, after having directed the telescope to the 



238 OF THE THEODOLITE. [CHAP. VII. 

pole at B, we may, instead of turning the vernier plate 
180°, let it remain unmoved, and reverse the telescope 
in its Y's, which will amount to the same. Proceeding 
thus from point to point, we may extend the line to 
any required distance. 



CHAPTER VIII. 



LEVELLING. 

The surface of an expanse of tranquil water or any 
similar surface concentric with it, is called a Level Sur- 
face. Any points situated in a level surface are said 
to be on the same level ; and any line traced in such a 
surface is called a line of level. 

If through any place, a level surface be conceived to 
pass, the distance which another place is from this sur- 
face, either above or below, measured on a line per- 
pendicular to it, is called the difference of level of the 
two places. 

Levelling is the art of determining the difference or 
differences of level of two or more places. 

In consequence of the globular figure of the earth, a 
level surface is not, as it appears to be, a plane surface. 
It is nearly, though not exactly, spherical. In the ope- 
rations of levelling we may, without sensible error, 
regard a level surface at any place, as being strictly a 
spherical surface, with a radius equal to 3956 miles, 
the mean radius of the earth, or, which is more exact, 
with a radius equal to 3968 miles ;* the centre being 

* The earth, if we disregard the inequalities in its surface, is an oblate 
spheroid. Its polar diameter is 7899 miles, and its eauatorial diameter 
7925 miles. A level surface is therefore a spheroidal surface. The radius 
of the spherical surface which most nearly coincides with any small portion 
of this spheroidal surface, changes slightly with the latitude of the place. 
For any place in the United States, the greatest error which can occur from 

239 



24v LEVELLING. [CHAP. VIII. 

in a straight line conceived to be drawn downwards 
from the place, perpendicular to the level surface. And 
for places not very remote from each other, we may 
regard the spherical surfaces of level passing through 
♦hem, as having a common centre. 

Let A and B, Fig. 120, be two places, not very 
remote from each other, and C, the common centre of 
the spherical surfaces of level passing through them. 
With the centre C and radius CA, describe the arc Aa. 
Then will Aa be a line of level of the place A, and Ba 
will be the difference of level of the two places A and B. 

The line Aa 7 , drawn perpendicular to CA, is called a 
line of apparent level of the place A. It is the line of 
level that would be indicated by an accurately adjusted 
levelling instrument placed at A. The distance ad is 
called the correction of the apparent level. This correc- 
tion must be subtracted from the height Bd of the ap- 
parent level to obtain the height Ba, of the true level. 
The correction varies as the square of the distance 
from the place.* The following table contains the 

considering the level surface passing through it, as a spherical surface with 
a radius equal to the mean radius of the earth, is about I of an inch for a 
distance of two miles. For a spherical surface with a radius 5 or 6 miles 
greater than the equatorial radius of the earth, the greatest error is about T \ 
of an inch, at the same distance. It may be further observed, that the 
greatest error or greatest deviation of the spherical from the spheroidal sur- 
face, varies as the square of the distance from the place. 

* We have (36.3), (2Ca -f- ad), ad — Ad" 1 . But as ad, for any distance 
to which a single sight in levelling is ever extended, is extremely small in 
comparison with 2Ca, we may, without sensible error, take 2Ca instead of 

A ,72 

(2C« -f ad). We shall thus have 2Ca, ad —Ad"; or ad* = — . Conse- 

2Ca 

quently as Ca is constant, ad varies as the square of the distance Ad varies. 

Let the value of ad be required for a distance of 100 chains or 6600 feet. 

Then taking Ca = 3968 miles, we have 2Ca = 7936 miles = 7936 x 5280 



CHAP. VIII. J LEVELLING. 241 

value of the correction in decimal parts of a foot, for 
each chain of distance, from 1 to 120. 

TABLE, 

Giving the differences between the true and apparent level, 
for distances from 1 to 120 chains. 



Chains. 


Feet. 


Chains. 


Feet. 


Chains. 


Feet. 


Chains. 


Feet. 


Chains. 


Feet. 


1 


.000 


25 


.065 


49 


.250 


73 


.554 


97 


.978 


2 


.000 


26 


.070 


50 


.260 


74 


.569 


98 


.998 


3 


.001 


27 


.076 


51 


.270 


75 


.585 


99 


1.019 


4 


.002 


28 


.082 


52 


.281 


76 


.600 


100 


1.040 


5 


.003 


29 


.087 


53 


.292 


77 


.616 


101 


1.060 


6 


.004 


30 


.094 


54 


.303 


78 


.632 


102 


1.082 


7 


.005 


31 


.100 


55 


.314 


79 


.649 


103 


1.103 


8 


.007 


32 


.106 


56 


.326 


80 


.665 


104 


1.124 


9 


.008 


33 


.113 


57 


.338 


81 


.682 


105 


1.146 


10 


.010 


34 


.120 


58 


.350 


82 


.699 


106 


1.168 


11 


.013 


35 


.127 


59 


.362 


83 


.716 


107 


1.190 


12 


.015 


36 


.135 


60 


.374 


84 


.734 


108 


1.213 


13 


.018 


37 


.142 


61 


.387 


85 


.751 


109 


1.235 


14 


.020 


38 


.150 


62 


.400 


86 


.769 


110 


1.258 


15 


.023 


39 


.158 


63 


.413 


87 


.787 


111 


1.281 


16 


.027 


40 


.166 


64 


.426 


88 


.805 


112 


1.304 


17 


.030 


41 


.175 


65 


.439 


89 


.823 


113 


1.327 


18 


.034 


42 


.183 


66 


.453 


90 


.842 


114 


1.351 


19 


.038 


43 


.192 


67 


.467 


91 


.861 


115 


1.375 


20 


.042 


44 


.201 


68 


.481 


92 


.880 


116 


1.399 


21 


.046 


45 


.211 


69 


.495 


93 


.899 


117 


1.423 


22 


.050 


46 


.220 


70 


.509 


94 


.919 


118 


1.447 


23 


.055 


47 


.230 


71 


.524 


95 


.938 


119 


1.472 


24 


.060 


48 


.240 


72 


.539 


96 


.958 


120 


1.497 



feet. Hence ad - 



6600* 



100 2 X 66 2 



= 1.0396 ft. 



7936 X 5280 7936 X 5280 7936 X 
Having the correction for 100 chains, we easily obtain it for any other 
distance by the following proportion : As 100 2 : square of given distance in 
chains : : 1.0396 : the required correction, in feet. 
21 2H 



242 LEVELLING. [CHAP. VIII. 

When a ray of light passes obliquely through por- 
tions of air of different densities, it becomes bent from a 
straight line, and enters the eye so as to make the point 
from which it proceeds appear in a direction slightly 
different from its true direction. This effect is called 
Refraction; and when the point, or body from which 
the light proceeds, is on or near the earth, it is called 
Terrestrial Refraction. Terrestrial Refraction generally 
makes the point appear to be more elevated than it 
really is. Thus it is not actually the point d of the 
line CE, Fig. 120, that, to an eye at A, appears to be 
at d, but another point c, a little below d. If therefore 
we wish to notice the effect of refraction, we must take 
ac instead of ad, for the correction of apparent level. 
In temperate climates, cd is, in the usual state of the 
atmosphere, about i of ad. Consequently we may ob- 
tain the correction of apparent level with allowance for 
refraction, by diminishing the correction given in the 
preceding table by a e part. 

As the effect of refraction in the common operations 
of levelling is always small, and is subject to considera- 
ble variations depending on the state of the air between 
the object and place of observation, it is commonly dis- 
regarded. It v^oulcl, however, in general be better to allow 
for it as above, except when the object is but little distant 
from the place of observation, or when, by the method 
noticed in the next article, the desired result is obtained 
independently of the correction of apparent level. 

Let CD, Fig. 121, be the line of apparent level indi- 

Fig. 121. 

0\ -^ ; :;::,. ; .^_, = ^ /> 



cated by a levelling instrument L, placed midway be- 
tween the places A and B ; also let the arc be be the 



CHAP. VIII.] LEVELLING, 243 

line of true level passing through the instrument, the 
arc Aa, concentric with the former, the line of true 
level of the place A, and AC and BD, lines perpen- 
dicular to Aa. Then in consequence of the equality 
of the distances LC and LD, we have 5C equal to 
cD; and therefore as A5 is equal to ac, we have AC 
equal to aD. Consequently Ba, the difference of level 
of the places A and B, is obtained by subtracting AC, 
the height of the apparent level of the instrument, at 
A, from BD, its height at B. We thus obtain the dif- 
ference of level of the two places, independently of 
the correction of apparent level. It is also indepen- 
dent of refraction, as the effect of refraction would be 
sensibly the same for the two points C and D, and in 
the same direction. It may be observed that it is not 
necessary the instrument should be directly between 
the places. It may be placed in any convenient po- 
sition on either side of the line joining them, pro- 
vided its distances from the places are equal, or very 
nearly so. 

OF THE LEVELLING INSTRUMENT. 

The Levelling Instrument, or Level as it is frequently 
called, is an instrument used to denote the line of ap- 
parent level. It is supported, like the theodolite, on a 
tripod. The instrument, without the tripod, is repre- 
sented in Fig. 119. Its lower part is nearly similar to 
the corresponding part of the theodolite. The plate 
HH, which screws on the tripod, has four levelling- 
screws inserted in it, by means of which the plate GG 
may be placed in a horizontal position, even when the 
former is considerably inclined. S is a clamp-screw, 



244 LEVELLING. [CHAP. VIII. 

and O a tangent-screw. The bar EE is firmly at- 
tached at right angles to an axis, which terminates in 
a ball, enclosed in the socket R. In some instruments 
this bar is enlarged at the middle so as to form a com- 
pass box, in which a magnetic needle is placed. The 
telescope AB is supported on two wyes, Yl and Y2. 
one of which, Yl, is firmly connected with the bar 
EE, and the other, Y2, is moveable a small distance 
up or down by the screw N, or in some instruments 
by two screws, M and P. The eye-tube L is move- 
able in or out by hand, so as to render the spider's 
lines distinctly visible, and the tube which contains 
the object-glass is moved by turning the milled head 
d, and may thus be so adjusted as to give distinct 
vision of an object to which the telescope is directed. 
One end, C, of the spirit-level CD is moveable up or 
down by the screw m, and the other end is moveable 
laterally by two opposite screws p and y, of which 
only p appears in the figure. 

The following adjustments of the level should be 
examined, and corrected if necessary, before using it 
in practical operations. 

FIRST ADJUSTMENT. 

To make the line of collimation coincide with the axis of 
the telescope. 

Having screwed the level to the tripod and set up 
the instrument so as to stand firmly, loosen the clamp- 
screw, turn the telescope towards some distant well- 
defined object, and fasten the screw. By means of 
the tangent-screw move the telescope slowly till the 



CHAP. VIII.] LEVELLING. 245 

line of collimation is directed exactly to some distinct 
point in the object, and then proceed according to the 
instructions in the second paragraph of the first ad- 
justment of the theodolite. 

SECOND ADJUSTMENT. 

To make the axis of the level CD parallel to the line of 
collimation. 

By turning the screw N, bring the bubble of the 
level to stand at the middle of the tube. Reverse the 
telescope in its wyes, and, if the bubble does not then 
stand in the middle, correct one half of the deviation 
by the screw m, and the other half by the screw N. 
Again reverse the telescope in its wyes, and repeat the 
correction if necessary. 

Now by revolving the telescope in its wyes, bring 
the level to some distance on one side of its lowest 
or proper position, and if the bubble then deviates from 
the middle, the deviation must be corrected by means 
of the screws p and g, which move one end of the 
level laterally, the correction being continued till the 
bubble will remain at the middle while the telescope 
is revolved so as to bring the level to a considerable 
distance on either side of its lowest position. When 
this has been done, the first part of the adjustment 
should again be examined and corrected if neces- 
sary.* 

* A method by which the second adjustment may be made for an instru- 
ment in which the telescope is not reversible, will be found in the first of 
the following problems. 



21* 



246 LEVELLING. [CHAP. VIII. 



THIRD ADJUSTMENT. 

To make the line of collimation parallel to the bar EE, 
or which is the same, at right angles to its axis. 

Turn the telescope till it stands directly over two 
of the levelling-screws, and by means of them bring 
the bubble to stand at the middle of the tube. Then 
turn the telescope half round, that is, till it stands 
over the same screws, but pointing in the opposite 
direction, and if the bubble does not remain in the 
middle, correct one half of the deviation by the level- 
ling-screws and the other half by the screw N. Now 
place the telescope over the other levelling-screws, and 
proceed in a similar manner. Continue the correc- 
tions till the bubble will remain in the middle of the 
tube during an entire revolution. 

These adjustments having been carefully made, the 
instrument is ready for use. When on the ground it 
must, in each new position in which it is placed, be 
levelled. This is done by placing the telescope over 
two of the levelling-screws and by their means bring- 
ing the bubble of the level to the middle of the tube, 
then doing the same with the telescope over the other 
two, and again over the first two. Then, if the third 
adjustment has been accurately made, the bubble will 
stand in the middle of the tube in any position of the 
telescope. 

OF THE LEVELLING STAFF. 

A Levelling Staff consists of a square or rectangu- 
lar staff and a small circular or rectangular board, 



CHAP. VIII.] LEVELLING. 247 

called a Vane, which is so attached to the staff as to 
be moveable along it from end to end. It is used for 
measuring the height of the line of apparent level 
passing through the telescope of the levelling instru- 
ment, above the place where the staff is placed. 

The face of the vane, represented in Fig. Ill, is 
divided into four equal parts by two straight lines 
intersecting each other at right angles ; one line being 
horizontal, and consequently the other vertical. Two 
opposite parts of the face are painted white and the 
other two black; thus the lines and their intersection 
are easily distinguished even at a considerable dis- 
tance. A screw, the head of which is shown at m, 
serves to clamp the vane to the staff in any required 
position. 

The staff is composed of two rectangular bars of 
wood, between five and six feet long, placed side by 
side, and forming together a square staff, the breadth 
of each side of which is about an inch and a quarter. 
The bars are so connected that one, which is two or 
three inches the shorter of the two, may be made to 
slide along the other or principal bar, and thus, when 
necessary, increase the length of the staff. In order 
to this, the front or sliding bar has throughout its 
length, on the side next the other, a projection which 
is terminated by a brass plate a little wider than the 
projection and firmly attached to it ; and the principal 
bar has a groove in it to receive the projection and 
plate of the former. The forms of the projection 
and groove are exhibited in Fig. 112, which repre- 
sents a section of the bars, at right angles to their 
length. 



248 LEVELLING. [CHAP. VIII. 

The staff is represented in Fig. 113, in which beef a 
is the principal bar, which is capped at the bottom 
with a brass plate ; bd is the sliding bar, A is the vane, 
seen edgewise, and n is a screw which serves to clamp 
the bars together in any given position. One side of 
each bar is divided, from bg upwards, into feet and 
hundredths of a foot ; the feet being numbered as in 
the figure. The subdivisions of the feet are omitted 
as they could not well be all exhibited. On the cham- 
fered edge of a brass plate connected with the vane, a 
fine line a is drawn, directly opposite to the horizontal 
line of the vane. The line a serves therefore to de- 
note on the side of the principal bar, the height that 
the vane is above the line bg, when that height does 
not exceed 5 feet. 

The height of the vane above the line bg is usually 
called the height of the cane, although it is less than 
its true height above the ground or place on which 
the staff stands, by the length of the part be. This 
however produces no error in the use of the staff in 
levelling, as the difference in level of two places is 
found from the difference in the heights at the places, 
of a line of apparent level passing through the level- 
ling instrument, and this difference will evidently be 
the same whether both heights are measured from the 
ground, or both from the line bg. 

When it is required to raise the vane to a greater 
height than 5 feet, it must be slid up to a pin at />, 
which checks it at that height, and be fastened there 
by the screw m, Fig. 111. Then loosening the screw 
u, Fig. 114, the front bar, which carries the vane, may 
be slid upwards till the vane acquires the required 



CHAP. Vm.] LEVELLING. 249 

height. When this is done, that point on the graduated 
side of the sliding bar, which corresponds to the line 
marked 5, on the principal bar, will evidently indicate 
the height of the vane. 

SCHOLIUM. 

The theodolite, levelling-instrument, and levelling- 
staff, are made of various forms and of different de- 
grees of perfection. Those which have been described 
are, when well made, good and convenient instruments ; 
and from the descriptions which have been given of 
them, the student will find it easy to understand the 
manner of adjusting and using others which may differ 
from them in form. 

PROBLEM I. 

To test the adjustment of the level. 

Select a place where the ground is tolerably level for 

a distance of 15 or 20 chains, and at each extremity 

of the distance chosen, as at A and B, Fig. 122, drive 

Fig. 122. 



a short stake. Set up the level by the stake at A, 
placing it so that the eye-end of the telescope may 
be over or nearly over the stake, and level the instru- 
ment. Place the levelling-staff on the stake, raising 
or lowering the vane till its horizontal line is at ex- 
actly the same height as the centre of the eye-end of 
the telescope, and note the height. Now let an as- 
sistant take the staff and set it up vertically on the 
stake at B. Direct the telescope to the middle of the 
breadth of the staff, and then, by raising or lowering 
the hand as a signal, direct the staff-bearer to raise or 
21 



250 LEVELLING. [CHAP. VIII. 

Jowei the vane, repeating the signal till its centre ap- 
pears precisely in the direction of the line of collima- 
tion, or at least exactly of the same height. When 
this is the case, by a circular motion of the hand, 
direct the vane to be clamped, and again sight to it 
to ascertain that in clamping, its height has not been 
changed. Note the height of the vane, and subtract 
from it the correction of apparent level corresponding 
to the distance between the stakes, taken from the 
preceding table, or rather this correction diminished 
by a } part, to allow for refraction. Then, if the 
instrument is accurately adjusted and the observations 
have been carefully made, the difference between the 
height of the vane at A, and its corrected height at 
B, will be the true difference of level of the tops of 
the two stakes; the higher being that at which the 
height of the vane is the less. Placing now the in- 
strument at B, proceed in the same manner to find 
again the difference of level of the stakes. If this 
difference is the same as the former, the adjustment of 
the instrument is correct. But if there is any mate- 
rial difference in the two results, we infer that the 
axis of the level is not parallel to the line of collima- 
tion. To make it so, take half the difference of the 
results obtained, and let the vane, taken in its last po- 
sition, be elevated or depressed by that quantity, accord- 
ing as the result obtained at the more elevated of the 
two stakes, is less or greater than that obtained at the 
other.* Then, by the screw N, bring the line of colli- 

* Let ah be the line of apparent level through the instrument when placed 
at A, and ae, the line of apparent level indicated by the instrument. Then 
cd being the line of apparent level through the instrument when placed at 
B, the line cf making the angle fLd equal to bhe, and consequently dj 
equal to be, will be the line of apparent level indicated by the instrument. 



CHAP. VIII.] LEVELLING. 251 

mation to point exactly to the horizontal line of the 
vane, and with the telescope in that position, bring the 
bubble again to the middle of the tube by the screw m. 

Note. In this manner the axis of the level may be 
made parallel to the line of collimation when the tele- 
scope is not reversible, as is the case in some instru- 
ments. 

EXAMPLE. 

Let the height Aa, be 5.295ft. f Be, 2.063ft.; Be, 
5.527ft. ; and A/, 8.935ft. ; and the horizontal distance 
from A to B, 20 chains. 

The distance being 20 chains, the correction for ap- 
parent level, taken from the table, is 0.042ft. From 
this deducting j of 0.042, we have 0.035ft. for the cor- 
rection to be subtracted from the heights Be and A/! 
This gives, for the corrected heights, Be = 2.028ft., and 
Af = 8.900ft. Hence, taking 2.028 from 5.295, we 
have 3.227ft. for the true difference of level obtained 
with the instrument at A ; the place B being higher 
than A. And taking 5.527 from 8.900, we have 3,373ft. 
for the difference of level obtained with the instrument 
at B. Half the difference of these results gives 0.053ft. 
for the value of df, the error due to the error in the 

It is therefore evident that the difference of level of the two places obtained 
with the instrument at A, is less than the true difference by the quantity 
be, and the difference obtained with the instrument at B, is greater than 
the true difference, by the equal quantity df. Hence the difference of the 
two results must be twice df, the error in height produced by the error in 
the adjustment of the instrument. 

* Although the station staff is only divided to hundredths of a foot, we 
may with tolerable precision estimate the thousandths ; and when great 
accuracy is desired, it is better to do so. 



252 LEVELLING. [CHAP. VIII. 

adjustment of the instrument. Hence, as the difference 
of level given by the instrument at the more elevated 
place is greater than the other, the vane must be lowered 
0.053 ft. from its last height. The adjustment may 
then be made as directed. 



PROBLEM II. 

Fi s- 123 - To determine the difference 

■ -T- - r of level of tivo places, A 

JjS mmm!!! 00!^ and B, Fig. 123, when 
jM ^' u tliey are visible from each 

oilier and do not differ in level more than 8 or 10 feet. 

Place the level in some position C, about equally 
distant from the places, either in the line joining them 
or on either side as may be most convenient, and level 
the instrument. Let the staff-bearer set up the level- 
ling-staff at A, and having sighted to it and obtained 
the height of the vane at that station, let the staff be 
removed to B, and do the same. Then the difference 
of the two heights, without any corrections, will be 
the difference of level of the places ; that place being 
the higher, at which the height of the vane is the less. 

If the surface of the ground between the places is 
such that when the level is placed at equal or nearly 
equal distances from them, the line of apparent level 
of the instrument would pass below one place or too 
high above the other, as in Fig. 124, it may be placed 
in any position C, that will permit the sights to be 
taken to both places. Then, having measured the 
horizontal distances from A to C, and from C to B, we 
proceed as above, except that the observed heights Aa 
and Rb must be corrected by the differences between 
the true and apparent level, as taken from the table : 



CHAP. VIII.] LEVELLING. 253 

or, which is generally better, by the tabular quantities 
diminished by a i part. It may, however, be observed 
that when neither of the distances AC nor BC, exceeds 
five or six chains, the corrections are so small that they 
may be generally omitted. 

When a valley intervenes between the two places so 
that there is no suitable intermediate situation for the 
instrument, it may be placed at one of them ; and then 
the difference of level may be determined as in the pre- 
ceding problem. 

EXAMPLES. 

1. Let the observed height Aa, Fig. 123, be 7.343 ft. 
and Bb, 3.635 ft. ; then the difference of these, 3.708 ft. 
is the difference of level of A and B, the place B being 
higher than A. 

2. Let the observed height Aa, Fig. 124, be 8.457 ft. ; 

Fig. 124. 



Bb, 1.525 ft. : the distance from A to C, 24.1 ch.; and 



the distance from C to B, 8.2 ch. 



The correction for the distance 24.1 ch., taken from 
the table and diminished by a i part, is 0.050 ft., and 
for the distance 8.2 ch., it is 0.006 ft. The corrected 
heights are therefore Aa 8.407 ft., and Bb 1.519 ft. 
Hence the difference of level is 6.888 ft. 
22 



254 



LEVELLING. 



[CHAP. VIII. 



PROBLEM III. 

To find the difference of level 
of two places not visible from 
each other, or if visible, dif- 
fering considerably in level. 

Let A and F, Fig. 125, be 
the two places. Place the 
level in some position P, that 
will permit a sight to be taken 
to A, and also to some other 
place towards F, at about the 
same distance from the in- 
strument. Having levelled 
the instrument, let the staff- 
bearer set up the staff at A, 
and when the sight has been 
taken, let him note the height 
■jo of the vane as a first back- 
sight. Then let the staff be 
taken to some station B, about 
as far from the instrument as 
that is from the station A, 
and when the sight has been 
taken, let the height of the 
vane be noted as the first 
foresight. Next, the staff- 
bearer remaining at B, take 
the level to some suitable place Q, beyond B, and pro- 
ceed to take a back-sight to B, and then a fore-sight 
to a new station C. In the same manner the operation 
must be continued from C to D, from D to E, and from 
E to F ; the number of intermediate stations necessary 
to be taken, depending on the irregularities in the 




CHAP, vhl] levelling. 255 

ground and on the difference of level of the given 
places. 

Take the difference between the sum of the back- 
sights and the sum of the fore-sights, and it will be the 
difference of level of E and F; the place F being 
liiglier or lower . than A, according as the sum of the 
back-sights is greater or less than that of the fore- 
sights.* 

Note. — It is not necessary that either the interme- 
diate stations or the places of the instrument should 
be in the direct line between the given places; and 
frequently it will be found convenient to deviate con- 
siderably from that line. It may further be observed 
that although it is generally best to take each pair of 
the sights at equal or nearly equal distances, as the 
correction for apparent level is thus avoided, and also 
a slight deviation of the axis of the level from paral- 
lelism with the line of collimation will not then sensibly 
affect the accuracy of the result, yet sometimes in 
order to diminish the number of stations the sights are 
taken at unequal distances. When this is done, the 
distances must be measured and the sights be corrected 
as directed in such case, in the last problem. 

* Let GF lie a line of level through the place F ; then AG is the dif- 
ference of level of the two places A and F. Now we have, 

Sum of back-sights, 

= Aa + Bc + Ce + Dg + Vl=Aa + bc + Bb + Ce + I)g + '&l. Also, 

Sum of fore-sights, 

= Bb + Cd + J)f+'Eh + ~Em = Bb + Ce + ed + ~Dg + gf+'El + lh + F 
= ¥171 + 111 + gf+ed+Bb + Ce + J)g + 'El=qd + Bb + Ce + Dg + 'El 
=2)c + Bb + Ce + T)g + ~El=AG + Aa + bc + Bb + Ce + 'Dg + Rl 

The difference of these sums is AG, the difference of level of the places 
A and F. 



256 LEVELLING. [CHAP. VIET. 



EXAMPLE. 



Let the back-sights and fore-sights, Fig. 125, be as 
in the following table. 



Back-sights. 


Fore-sights. 


1. 7.103 ft. 


1.566 ft. 


2. 9.227 


3.178 


3. 1.236 


9.415 


4. 1.610 


6.367 


5. 2.125 


9.910 


Sum 21.301 


Sum 30.436 




21.301 



Diff. 9.135 

Hence the difference of level of A and F is 9.135 ft., 
and as the sum of the back-sights is less than that of 
the fore-sights, the place F is lower than A. 



CHAPTER IX. 



TOPOGRAPHY. 

Topography is a branch of surveying,* the object 
of which is to determine and designate on a map, the 
various undulations and inequalities in the surface of 
a particular place, tract of land or district of country. 
A map in which these inequalities, the courses of 
streams, and sometimes other circumstances, as the 
positions and extents of forests, marshes, &c, are de- 
signated, is called a topographical map. 

In addition to the boundaries and content of a tract 
of land, it is frequently required that the various slopes 
and irregularities of the surface should be determined 
and designated, in order to give a more complete view 
of the ground, and to afford the means for an appro- 
priate location of buildings or works of any kind that 
may be designed to be erected on it. 

If we assume the surface of a tract of land to be 
intersected by a number of level surfaces or horizontal 
planesf at equal distances from one another, and trans- 
fer all the lines of level in which these planes meet 
the surface of the ground to an assumed horizontal 



* The term surveying is here used in a more extended sense than as de- 
fined in the first chapter. 

f In tracts of any moderate extent, the surfaces of level may, for the 
purpose for -which they are here introduced, he regarded as horizontal 
planes. 

22 * 2 K 



258 T0P0GEAPI1Y. [CHAP. IX. 

plane passing through the lowest point, making them 
occupy positions on that plane, corresponding with 
their positions on their respective planes, the varia- 
tions in the distances of the lines from one another, 
when thus transferred, will indicate the variations in 
the inclination of the ground. For as the difference 
of level from line to line is the same, it is evident that 
the horizontal distances of the lines, taken in any di- 
rection, will diminish as the inclination in that direction 
increases. Thus in ABCD, Fig. 129, which represents 
a small tract, of which the length AB is 1000 feet and 
the breadth AD, 800 feet, the lines 10, 20, 30, &c, 
represent lines of level in which horizontal planes at 
the distance of 10 feet from one another, intersect the 
surface of the ground. The lowest level passes 
through the point F, at which the stream EF leaves 
the tract. From F the ground rises more rapidly to 
the left than to the right, as is indicated by the lines 
of level being nearer to one another on that side than 
on the other. In passing from F towards the corner 
B of the tract, we may observe that the acclivity, 
which is gentle, increases till we come to the 30 feet 
level, then diminishes to the 40 feet level ; it then 
again increases, and more rapidly, to the 60 feet level, 
and lastly slightly diminishes to the 70 feet, or highest 
level. In descending, the declivity continually dimin- 
ishes to B. From the point / in the side AD, the 
ground descends moderately towards the corner A, the 
declivity diminishing till the surface becomes nearly 
level ; and from the stream, towards A, the acclivity, 
which is slight, diminishes, so that between the two 
branches of the 30 feet line of level and the corner A. 
the ground is nearly level. 



CHAP. IX.] TOPOGRAPHY. 259 

The distance which should be taken for the distance 
of the assumed planes from one another, must depend 
on the extent of the survey, the inequalities in the sur- 
face, and the degree of minuteness with which it is 
required that they should be designated. It may vary 
from 3 or 4 to 20 or 30 feet, according to circum- 
stances. 

The levelling required for a topographical survey 
may be performed either with a level or theodolite. 
Where there is considerable ascent or descent in the 
ground, the latter is the most convenient instrument ; 
and although the results obtained with it are not in 
general as accurate as those that may be obtained 
with a good level, they are, when due care is taken, 
sufficiently so for the object in view. When the theo- 
dolite is used, the sight should be taken to a point at 
the same height above the ground at the station, as 
the axis about which the upper telescope revolves is 
above the ground at the place of the instrument. To 
do this, let an assistant place and clamp the vane of a 
levelling-staff at that height, or make a mark at the 
same height on a pole; and when he has taken the 
staff or pole to the station and set it up vertically, 
sight to the vane or mark. When this is done, the 
difference of level between the station and place of the 
instrument, expressed in 100th parts of the horizontal 
distance of the two, will be indicated on the vertical 
limb. It is however better, except when the horizon- 
tal distance is quite small, to obtain the difference of 
level from that distance and the angle of elevation or 
depression. 



260 TOPOGRAPHY. [c»AP. IX. 



PROBLEM I. 

Having given the back-sights and fore -sights taken to a 
number of consecutive stations, or to two or more con- 
nected series of stations, to determine the heights of the 
stations above a line of level or surface of level through 
the lowest. 

1. When there is but one series of stations. Assume 
for the height of the first station above some assumed 
line of level, any quantity taken at pleasure, observing 
however to make it sufficiently great for the assumed 
line of level to be lower than the lowest station, or at 
least as low. To the assumed height of the first sta- 
tion add the first back-sight, and from the sum subtract 
the first fore-sight, and the remainder will be the 
height of the second station above the assumed line 
of level. With this height and the second back-sight 
and second fore-sight proceed in like manner to find 
the height of the third station ; and thus on to the 
last. Now subtract the least of the heights obtained, 
which must be that of the lowest station, from each 
of the others, and the remainders will be the heights 
of the other stations above the line of level passing 
through the lowest. 

2. When there are two series of stations connected by 
intervening sights between the first station of the first 
series and the first of the second series. Assume for 
the height of the first station of the first series, a 
quantity sufficiently great for the assumed surface of 
level to be below all the stations, or at least as low ae 



CHAP. IX.] TOPOGRAPHY. 261 

the lowest, and proceed as directed above, to obtain 
the heights of the other stations of that series above 
the assumed surface of level. Then commencing again 
with the assumed height of the first station, proceed 
in like manner with the sights connecting that with 
the first station of the second series, and with the 
sights to the stations in this series, to find the heights 
of all these stations. When this is done, subtract the 
least of all the heights obtained from each of the 
others, and the remainders will be the required heights. 

3. In like manner, whatever be the number of the 
series of stations, the heights of all the stations, above 
a surface of level passing through the lowest, may be 
obtained. 

Note. If it is required to find the heights of the 
stations above a line or surface of level at a given dis- 
tance below the lowest or any other given station, it 
is easily performed by applying to the heights of the 
stations above the assumed level, the difference be- 
tween the height of that station above the assumed 
level and its height above the given level. 

EXAMPLES. 

1. Taking to the nearest length of a foot, the back- 
sights and fore-sights given in the example to the lasi 
problem of the preceding chapter, it is required to find 
the heights of the stations A, B, C, &c. Fig. 125, above 
a line of level passing through the lowest. 

Assume the height AL, of the station A, above an 
assumed line of level LM to be 15 feet. Then we 
have 



262 





TOPOGRAPHY. 




Feet. 






15, height of A, 


15 + 7.1- 


-1.6 = 20.5 


« B, 


20.5 + 9.2- 


-3.2 = 26.5 


" c, 


26.5 + 1.2- 


-9.4 = 16.3 


" D, 


16.3 + 1.6- 


-6.4 = 11.5 


" E, 


11.5 + 2.1- 


-9.9= 5.7 


a -p, 



[chap. IX. 



Subtracting 5.7 from each of the above heights, we 
have the heights above GF, the line of level through 
F. These are, for A, 9.3ft.; B, 14.8 ft.; C. 20.8 ft.; 
D, 10.6 ft. ; E, 5.8 ft. ; and F, ft. 

2. Let the back-sights and fore-sights, taken from A 
to B, Fig. 126, from A to C, and from C to D, be as 

Fig. 126. 



given below ; to find the heights of the stations along 
AB, AC, and CD, above a surface of level through the 
lowest station. 



AB 



AC 



CD 



B-sts. 


F-sts. 




B-sts. | F-sts. 


8.7 ft, 


3.8 ft. 


1 


8.5 ft. 5.2 ft. 


1.1 


9.9 


2 


0.6 9.1 


0.7 


9.3 




2.2 


8.0 




1.9 


7.1 




7.4 


4.2 







B-sts. 


F-sts. 


3.1ft. 


8.6 ft. 


2.6 


7.7 


1.5 


9.3 


4.2 


7.9 


3.8 


7.3 


9.3 


2.2 


2.8 


7.4 



By proceeding as directed in the rule, we obtain the 
following heights of the stations above the surface of 
level passing through the lowest. 



CHAP. IX.] 



TOPOGKAPHY. 



263 



AB 

30.8 ft. 
35.7 
26.9 
18.3 
12.5 
7.3 
10.5 



AC 

30.8ft. 
34.1 
25.6 



CD 

25.6 ft. 

20.1 

15.0 

7.2 

3.5 

0.0 

7.1 

2.5 



PROBLEM II. 

To determine the inequalities in the surface of the ground 
along a line running in a given direction, and to draw 
an irregidar or curved line to represent them. 

Let short stakes be driven at the beginning and end 
of the line, and at each point along it where there is 
any material change in the inclination of the ground ; 
and let the horizontal distance of each stake from the 
beginning of the line, or the distances from stake to 
stake, be measured. Then level from stake to stake, 
using intermediate stations whenever the difference of 
level between any two is too great to permit sights to 
be taken to both from a single position of the instru- 
ment. Find, by the last problem, the heights of the 
stations, where the stakes are placed, above a line of 
level passing through the lowest, or above any assumed 
or given line of level. 

Draw a straight line ef Fig. 127, to represent the 

Fig. 127. 




line of level to which the heights of the stations are 
referred, and on it make ea, eh, es, ec, &c, equal to the 
distances of the stations from the beginning of the 
line. From the points e, a, b, s, &c, draw lines per- 



264 



TOPOGRAPHY. 



[chap. 



IX. 



pendicular to ef, and make them equal to the heights 
of the respective stations. Through the tops of these 
perpendiculars, draw the curved line EF, which will be 
the line required to be drawn. 

The line EF is called a Profile of the ground in the 
direction of the given line. 

Note. The heights of the perpendiculars are fre- 
quently taken from a scale three or four times as great 
as that used in laying off the horizontal distances. 
When this is done, the curved line, or profile, as it is 
still called, indicates more distinctly the 'esser changes 
in the inclination of the ground. 



The distances of the stations along a given line, 
measured from the beginning of the line, and their 
heights above a given line of level, determined by the 
last problem, from sights taken on the ground, being 
as below, the profile of the ground in the direction of 
the line, obtained by taking the heights from a scale 
three times as great as that from which the distances 
are taken, will be that of Fie". 127. 



Sta. 


Dist. 


Ht. 




Sta. 


Dist. 


Ht. 


1 


Oft. 


41.1ft. 




8 


610ft. 


41.9ft. 


2 


90 


38.3 




9 


655 


55.0 


3 


230 


22.0 




10 


725 


69.2 


4 


336str. 


15.3 




11 


770 


72.0 


5 


445 


21.1 




12 


850 


69.1 


6 


505 


32.5 




13 


915 


56.5 


7 


555 


36.5 




14 


1000 


50.1 



CHAP. IX.] TOPOGRAPHY. 265 

At the fourth station a stream of water crosses the 
line, and is noted by the letters str. placed by the side 
of the distance. 

PROBLEM III. 

To determine those points along a line running in a given 
direction, that are at given heights above a given line 
or surface of level. 

Proceed, as directed hi the last problem, to find the 
heights above the given line or surface of level, of 
those points in the line where there is any material 
change in the inclination of the ground, and also their 
distances from the commencement of the line. Observe 
between which two of the heights obtained, any one 
of those given falls, and take their difference. Also 
take the difference between the given height and that 
one of the two which appertains to the point nearest 
the beginning of the line. Then, as the first difference 
: the second : : the horizontal distance between the 
points : to a fourth term, which added to the distance 
of the point nearest the beginning of the line, will give 
the distance of the required point. 

Proceed in the same manner with the other given 
heights. 

Or we may draw, by the last problem, a profile of 
the ground, as EF, Fig. 128, in reference to the given 

Fig. 128. 



40 30 20 S 20 30 40 50 60 70 70 60 60 

line of level ef, and on ea, perpendicular to ef set off 
the given heights, taking them from the scale used in 
setting off the heights of the stations. Then, through 
the points hi the line ea, draw lines parallel to ef, as 
23 2L 



266 TOPOGRAPHY. [CHAP. IX. 

in the figure ; and from the points in which these meet 
the profile EF, draw lines parallel to ea. The dis- 
tances from e, at which these last lines meet ef will 
be the horizontal distances of the required points, from 
the beginning of the line. 



EXAMPLE. 



Let the data found on the ground be the same as 
in the example to the last problem, and let the given 
heights of the required points be 10, 20, 30, 40, &c. 
feet. 

The distances and heights of the stations being the 
same as for the profile in Fig. 127, we shall obtain a 
similar profile EF, Fig. 128. Drawing the lines paral- 
lel to ef at distances from it, equal to 10, 20, 30, &c. 
feet, we find that the first line above ef does not meet 
the profile EF. Consequently there is no point in the 
latter so low as 10 feet above the given level. Each 
of the other parallels meets the line EF in two points. 
There are therefore two points in the line at the height 
of 20 feet above the given level ; two at the height of 
30 feet ; and so on to 70 feet. The distances e, 40 ; 
e, 30 ; &c, on the line ef are the distances of the 
required points from the beginning of the line. 

In illustration of the first method of finding the dis- 
tances of the required points from the beginning of 
the line, as the given heights of the stations evidently 
show that there is no point in the line so low as 10 
feet above the given level, let it be required to find a 
point at the height of 20 feet. On examining the 
given heights of the stations, we perceive that there 
must be two such points ; one between the 3d and 



CHAP. IX.] 



TOPOGRAPHY. 



267 



4th stations, and one between the 4th and 5th. For 
the first of these we take the difference between 15.3 
and 22.0, which is 6.7; the difference between 20.0 
and 22.0, which is 2.0 ; and the difference between the 
distances 230 and 336, which is 106. Hence, as 6.7 : 
2.0 : : 106 : 32. Adding therefore 32 to 230, we have 
262 feet for the distance of this point. 



PROBLEM IV. 

To determine the undulations and inequalities of the sur- 
face in a tract of land ABCD, Fig. 129, and to draiv 
a topographical map designating them. 



Fig. 129. 




With a compass or theodolite, run a number of lines, 
ah, cd, ef &c, across the tract, parallel to one of the 
sides, as AB ; making them nearer together or farther 
apart, according to the inequalities in the ground and 
the degree of minuteness with which it is intended to 
designate them. Drive stakes at the beginnings and 
ends of the lines AB, ah, cd, &c, and at all the points 
along them where there is any material change in the 
inclination of the ground, and proceed to level from 



268 TOPOGRAPHY. [CHAP. IX. 

stake to stake along these lines and the line AC ; also 
measure the distances of the stakes from the com- 
mencement of the lines, or from one another. Then, 
by problem I., find the heights of all the stations where 
the stakes are driven, above a surface of level passing 
through the lowest station. 

Now, having drawn the lines ah, cd, ef, &c, in their 
proper positions on the map, determine, by the last 
problem, the points in these lines and the lines AB 
and DC, that correspond to heights in the lines on the 
ground, of 10, 20, 30, 40, &c, feet, above the surface 
of level passing through the lowest station, or to any 
other heights, increasing by equal differences, that may 
be deemed expedient. Through each set of points 
appertaining to the same height, draw a curve line. 
The curve lines thus drawn will represent lines of 
level of 10 feet, 20 feet, &c, or of the number of feet 
of the heights used in obtaining them, whatever that 
may be. 

These lines serve to indicate the changes in the 
inclination of the ground. But it is usual, instead of 
drawing them distinctly with ink, to draw them with 
a pencil only, or faintly with Indian-ink, and then to 
shade the map by short straight lines, drawn perpen- 
dicularly from each curve of higher level, to that of 
the next lower ; the lines being drawn closer together 
and rather heavier as the distance between the lines 
of level diminishes. For those parts of the ground that 
are level, or very nearly so, the shading is omitted. 
The greater or less darkness of the shading on the dif- 
ferent parts of the map, therefore, indicates a greater 
or less inclination in the ground in those parts ; and 
the omission of the shading in any parts, indicates that 



CHAP. IX.] 



TOPOGRAPHY. 



269 



in those places the surface is level, or very nearly so. 
In Fig. 130, we have a map of the tract, shaded as 
described above. 




Note. — It is not necessary that the lines on which 
the levels are taken should be run parallel to one 
another. They may be run making given angles with 
any given lines of the survey. Sometimes it is desired 
that the surface of a particular part of the tract should 
be designated with more minuteness than is important 
for other remote parts. In this case it will be found 
convenient to determine the position of some point 
near the middle of the part which it is desired par- 
ticularly to designate, and then to run hues from this 
point, in directions making angles of 20° or 30° with 
one another. 



It may be further remarked, that instead of taking 
the surface of level through the lowest point, as the 
plane of reference, we may, if preferred, take that 
through the highest. The former is however the one 
generally taken. 
23* 



270 TOPOGRAPHY. [CHAP. IX. 

The operations to be performed in this problem, so 
far as observations on the ground and numbers are 
concerned, are merely repetitions of those which have 
been exemplified in the preceding problems. An ex- 
ample is not therefore necessary. 



HINTS TO YOUNG SURVEYORS. 



BY A PRACTICAL SURVEYOR. 



Young surveyors who have not had the advantage of 
instruction from careful practical operators often meet -with 
difficulties, and are much puzzled for want of the readiest 
means of overcoming them. In such cases, it is all im- 
portant to keep themselves cool and collected ; otherwise they 
may expect to be pestered with officious suggestions or mortify- 
ing remarks from the lookers-on, thus adding to their confusion, 
and rendering the chance of overcoming the difficulty more 
uncertain. It is presumed that young men undertaking the 
business have made themselves familiar with all the necessary 
calculations : in which event a little practice will enable them 
to adapt the proper means to the circumstances of the case. 

A few examples are here inserted, embracing some of the 
obstructions which most frequently occur in the practice, with 
a view to familiarize the student with them, in order that he 
may at the outset be the better able to encounter them. 

Example 1. Fig. 1. 

A. has agreed to convey to B. a part of his tract of land, 

situate in the township of , county of M , state 

of D , at a certain price per acre. The parties having 

fixed upon the several corners A, B, C, D, E, F, Gr, and H, call 
upon Q. to survey it, and make out a description to be recited 
in the deed. 

After examining the ground, the corner at A is fixed upon 

(271) 



272 



HINTS TO YOUNG SURVEYORS. 



as the best place to commence. Placing the instrument at A, 
direct the telescope to. a staff placed perpendicular at B, a 




stone for a corner ; ascertain the bearing of AB, N. 48° 32' 
W. The line AB runs through a pond of water, and cannot 
be measured with a chain. The distance must therefore be 
ascertained by trigonometry. From the point A measure any 
angle, say 21°. West of the line AB measure any distance 
on this line, say 80 P. to a. Place the transit at A, and 
measure the angle AaB, which proves to be 139° 38', the angle 
ABa is therefore 19° 22'. Now we have the three angles and 
one side of the triangle ABa, to find the side AB, which is 
found to be 156.25 P. 

The corner C is a spike driven near the middle of a white 
oak stump. It cannot be seen from B, nor can the points B 



HINTS TO YOUNG SURVEYORS. 273 

and G be seen from any intermediate place, on account of hills 
intervening. Place the instrument at B, and run a random 
line as near the direction of C as you can judge, say S. 51° 
35' W. ; measure this line. At 40 P. it crosses a small run 
of water. Thence 62.8 P. to a point opposite C (whole dis- 
tance 102.8). The line is 8 links East of the point C, the 
difference therefore of the bearing of the true line is 10' West 
of the random line, or S. 51° 45' W., 102.8 P. 

The corner at D is a hole in a high rock, and cannot be 
measured to with the chain. You must therefore resort to trigo- 
nometry. From C, the corner at T> bears N. 41° 5V W. 
With this line measure any angle, say 40°, to the East ; measure 
any distance on this line, say 92 P. to a point where you can 
see objects at C, D, and E (marked b). From b measure the 
angle C6D which proves to be a right angle, and D5E, which is 
112° 84'. Measure the line 5E, 84.62 P. to a stake in the 
middle of a public road. You have now one side and two 
angles of the triangle CbD, to find the side CD, which is 
120.1 P., and the side bB, which is found to be 77.2 P. And 
two sides and enclosed angle of the triangle D5E, to find the 
side DE and its bearing, N. 52° 41' E. 134.8 P. From E you 
proceed along the middle of the road S. 71° 42' E. 14.5 P. to 
a small run of water, and 76.62 P. to another stake in the 
middle of the road. Thence S. 84° 16' E. 52.48 P. to a stone 
at G. The next line, GH, is inaccessible in consequence of 
thick bushes and trees, extending nearly its whole length. 
Measure back any distance on your last line that will give you 
a clear sight, say 8 P. to e, and from H on the same course, 
measure 8 P. to d, and place a staff there. From C you ascer- 
tain the course cd, which is parallel with GH, to be S. 51° 42' 
E., measure the distance from e to d, which is 144.2 P. If the 
staff has been placed in the proper direction from H, the dis- 
tance of GH will be equal to cd. Test this by placing the 
instrument at d, and take the bearing of FG, S. 84° 16' E., 
this strikes 5 links short of the corner at H. I must there- 
fore add 0.2 P. to the length of the line cd, for the length of 
GH. GH is therefore S. 51° 42' E., 144.4 P. The last line 
HA cannot be measured, or its bearing taken from either end. 
It is, however, ascertained by traversing the survey to be S. 
42° 42' W. 94.72 P. 

2M 



274 HINTS TO YOUNG SURVEYORS. 

The accuracy of the work may be tested by calculating the 
bearing and distance of the corner H or A from either of the 
other opposite corners. Thus : In the triangle ABH, you have 
the two sides and their bearings, to find the bearing and distance 
of the line BH. This having been found by calculation to be 
S. 79° 13' E., 185.6 P., the instrument placed upon B and 
directed to H will test the accuracy of the whole survey. 

In making out the description for the conveyancer, it is best 
to commence at some well-defined corner of the survey. This, 
however, is a mere matter of convenience. The description 
of the above may be as follows. 

Beginning at a stake set for a corner in the middle of a 

public road leading from R to C , at the distance of 

82.6 P. south-eastward from a stone, a corner of John Dunn's 
land. Thence along the middle of said road S. 71° 42' E., 
91.12 P. to a stake, and S. 84° 16' E., 52.48 P. to a stone for 
a corner. Thence by land of Peter Binder, S. 51° 42' E., 
144.4 P., to a white oak sapling marked. Thence by land of 
John White, S. 42° 42' W., 94.72 P., to a stone set for a 
corner. Thence by other ground of the said A., N. 48° 32' 
W., 156.25 P., crossing a pond of water to a stone for a corner. 
Thence still by said A.'s land, N. 51° 45' W., 102.8 P., to a 
spike in a white oak stump. Thence by same land, N. 41° 51' 
W., 120.1 P. to a hole in a rock, in a line of Peter Dunn's 
land. Thence by said land, N. 52° 41' E., 134.8 P., to the 
place of begnining. Containing 222 A. 3 qr. 23 P. of land. 



example 2. 

It is required to survey a piece of ground described as 
follows : 

Beginning at a corner in the middle of a road leading from 

H to B . Thence by ground of W. B. C, N. 50° 30' 

W., 74.24 P. to a black oak tree for a corner. Thence by land 
of A. G., S. 40° W., 204 P. to a stone. Thence by the same 
land, S. 84° 30' W., 48.4 P. to a white oak tree, standing by 

the bank of P creek, and 1 P. to the middle of the creek. 

Thence up the said creek, the several courses, 42.5 P. Thence 
by ground of J. A., N. 40° E., 1 P., to a pin oak on the 



HINTS TO YOUNG SURVEYORS. 



275 



bank of said creek, and 32.8 P. to a corner. Thence by ground 
of J. F., S. 50° 30' E., 18.8 P., to a stone, and N. 38° 30/ 
38.4 P. to a stone. Thence by land of J. N., S. 50° 30' E., 
93.2 P. to a corner in the middle of said road. Thence along 
the said road, S. 1° 45' E., 51.4 P. to the place of beginning. 
Containing 45 acres of land more or less. 




Upon examining the ground, I do not find any of the land- 
marks that may be depended upon, except the stones at the 
two ends of the line GH [See plan). These are firm in the 
ground, and have each a small hole near the centre. This 
line is recited N. 38° 30' E., 38.4 P. I find the bearing 
at the present time to be N. 37° 42' E., consequently the 
variation of the needle since the former survey, is 48' W. I 
measure the line GH, and find it to correspond with the former 
measure, 38.4 P. 

It rarely if ever happens that the bearings of recent surveys 
correspond with those of the same lines taken years back, and 
very generally there is a difference between the old and recent 
measures of lines. It is best to make the corrections, as well 
of the bearings as of the distances of the whole survey before 
proceeding further, in order to have as little calculating as 
possible during the survey. Some surveyors rule a table with 



276 



HINTS TO YOUNG SURVEYORS. 



four columns like the following, placing the recited bearings 
in the first, corrected bearings in the second, recited distances 
in the third, and corrected distances in the fourth, thus : 



Recited 
Bearings. 


Corrected 
Bearings. 


Recited 
Distances. 


Corrected 
Distances. 


N. 50° 30' W. 


N. 51° 18' W. 


74.24 


74.62 


S. 40° W. 


S. 39° 12' W. 


20.4 




S. 84° 30' W. 


S. 83° 42' W. 


48.4 




Creek. 








N. 40° E. 


N. 39° 12' E. 


32.8 




S. 50° 30' E. 


S. 51° 18' E. 


18.8 




N. 38° 30' E. 


N. 37° 42' E. 


38.4 


38.6 


S. 50° 30' E. 


S. 51° 18' E. 


93.2 




S. 1° 45' 


S. 2° 33' E. 


51.4 





The variation being found to be 48' W., the bearings are 
corrected by adding 48' to NW and SE, and deducting 48' from 
the SW and NE courses. 

If the measure of the line between the two stones do not 
correspond with the recited measure, make the correction of 
all the lines in that proportion, and place the result in the 
4th column. 

Thus, suppose GH should measure 38.6 P., place that in 
the 4th column, opposite the line GH. Then, as 38.4 : 38.6 
: : 74.24 : 74.62, &c. 

The old and new measures agree in the present case, there- 
fore the 4th column is unnecessary. 

Having ascertained the bearing and distance of the line GH, 
I proceed from H to I. I take my course S. 51° 18' E., and 
measure upon that course 73.2 P. which is 20 perches short 
of the distance required, where I meet with a thicket through 
which I cannot see or measure. From this point, marked d, 
and with the line a, I measure an angle of 60°, and measure 
20 P. to b. From be and with the line ba I measure an angle 
of 60° and measure 20 P., which must bring me to I, where 



HINTS TO YOUNG SURVEYORS. 277 

I put a stake, the old land-mark being lost. From I to A 
there is no obstruction. I therefore place the instrument at 
I, and direct the telescope S. 2° 33' E., and measure 51.4 P. 
At this point we find a stone corresponding with the last course 
and distance ; this proves the correctness of the stake at I. 
The line AB is inaccessible ; I therefrom run a line parallel 
with BC (S. 39° 12'), 20.4 P., marked c. From C I run a line 
parallel with AB (N. 51° 18' W.) 74.25 P. to C, a stone. 
From C run a line N. 39° 12' E. 20.4 P. to B ; this was for- 
merly a black oak tree. The tree is gone, but the stump 
remains. From C I run a line S. 83° 42' W. 42.98 P., which 
brings me to a white oak tree on the bank of the creek, and 
1 P. to the middle of the creek. 

I now return to the stone at Gr, and run a line from Gr, N. 
51° 30' "W"., 18.8 P. to F. The line EF is also inaccessible. 
I find by calculation that the point E should bear S. 68° 54' 
W. from G., 37.95 P. Run the line GE accordingly, and 
strike the pin oak tree recited in the deed, on the bank of the 
creek, and 1 P. from the middle thereof. From E I find D 
bears S. 19° 38' E., measure 42.98 P. At 10 perches from E 
make an off-set to the creek ; at the further distance of 20 P. 
make another off-set. The first off-set measures 3.2 P. to the 
middle of the creek, and the second 9.42 P. 

I find this tract to contain 45 A. 3 R. 27 P., including half 
the creek and half the road. 

It is best to place but little reliance upon the needle, and it 
may not be too much to say that it is impossible to complete 
a survey of any considerable tract of land with perfect accu- 
racy by the use of the needle alone. It is of great use, how- 
ever, and not to be altogether rejected. It is well to take the 
bearing of some one well defined line of the land to be surveyed, 
and by sighting back upon the lines as you advance, ascertain 
the other bearings by measuring the angles. 



Establishing Disputed Lines. 

This is the most delicate business that a young surveyor can 
undertake, and in which he should exercise the greatest care. 
A mistake in the early period of his practice may affect his 
24 



278 HINTS TO YOUNG SURVEYORS. 

reputation through life. In this branch, old surveyors, who 
are well acquainted with the neighbouring land-marks, have a 
decided advantage. But young surveyors need not therefore 
be discouraged. A little patience, and a little more trouble 
in finding the land-marks of the neighbouring tracts, which 
have a relation to the line in question, will enable him to come 
to as correct a conclusion as those who may presume upon 
their longer experience, and better knowledge, and take less 
care in their operations. It is not to be supposed that a sur- 
veyor by mere intuition, or some mysterious art, unknown to 
the uninitiated, can find out property lines or direct his com- 
pass with unerring certainty to a contested corner. He must 
be governed by the best evidence that the case will admit of, 
and should exercise due diligence to make himself acquainted 
with all the facts of the case. The best evidence of boundary- 
lines is monuments, such as stones firmly fixed in the ground, 
or trees known and acknowledged as land-marks. The next 
best is fences that have been for a long time received and 
acknowledged as lines, or ditch-banks thrown up to mark lines. 
Where no visible evidence is to be found on the ground, or 
where these are disputed, other means are to be resorted to. 

Before commencing to adjust a disputed line, it is advisable 
to examine the deeds as well of the lands which the line divides, 
as also the deeds of the lands adjoining these, and plot the 
whole upon a paper of convenient size to carry into the field, 
noting the recited land-marks upon the plan. If no definite 
marks are to be found upon the disputed line, it may be that 
it is part of a longer line. If satisfactory marks are to be 
found on the extended line, trace them to the line in dispute. 
If nothing of this kind is to be found, measure the lines which 
terminate in the disputed line, if definite starting points can 
be found. If not, these points must be found by tracing the 
other lines connected with them. Where care has not been 
taken to preserve ancient land-marks, it often becomes neces- 
sary to trace the lines of several adjacent tracts before any 
satisfactory conclusion can be arrived at. 

Roads. 

In tracing a road from the record, the same rules should be 
observed as in other surveys. It frequently happens that roads 



HINTS TO YOUNG SURVEYORS. 279 

have been laid out upon the lines dividing properties, and in 
many cases, the stones marking the lines of the road have been 
lost. In such cases their proper position must be found either 
by tracing the bearings and distances from the record, making 
allowance for the variation of the needle, or by measuring the 
property lines which terminate in the road. 



THE END. 



MATHEMATICAL TABLES 



DIFFERENCE 



LATITUDE AND DEPARTURE; 
LOGARITHMS, 

FROM 1 to 10,000; 



ARTIFICIAL SINES, TANGENTS, AND 

SECANTS. 



STEREOTYPE EDITION, CAREFULLY REVISED AND CORRECTED. 



TRAVERSE TABLE. 



o 

p 
a 
o 
? 

1 


i De S . 


i Deg. 


IDeg. 


d 

1 
» 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1.00 


0.00 


1.00 


0.01 


1.00 


0.01 


2 


2.00 


0.01 


2.00 


0.02 


2.00 


0.03 


2 


3 


3.00 


0.01 


3.00 


0.03 


3.00 


0.04 


3 


4 


4.00 


0.02 


4.00 


0.03 


4.00 


0.05 


4 


5 


5.00 


0.02 


5.00 


0.04 


5.00 


0.07 


5 


6 


6.00 


0.03 


6.00 


0.05 


6.00 


0.08 


6 


7 


7.00 


0.03 


7.00 


0.06 


7.00 


0.09 


7 


8 


8.00 


0.03 


8.00 


0.07 


8.00 


0.10 


8 


9 


9.00 


0.04 


9.00 


0.08 


9.00 


0.12 


9 


10 
11 


10.00 


0.04 


10.00 


0.09 


10.00 


0.13 


10 
11 


11.00 


0.05 


11.00 


0.10 


11.00 


0.14 


12 


12.00 


0.05 


12.00 


0.10 


12.00 


0.16 


12 


13 


13.00 


0.06 


1 13.00 


0.11 


13.00 


0.17 


13 


14 


14.00 


0.06 


14.00 


0.12 


14.00 


0.18 


14 


15 


15.00 


jQ-07 


15.00 


0.13 


15.00 


0.20 


15 


16 


16.00 


0.07 


16.00 


0.14 


16.00 


0.21 


16 


17 


17.00 


0.07 


17.00 


0.15 


17.00 


0.22 


17 


18 


18.00 


0.08 


18.00 


0.16 


18.00 


0.24 


18 


19 


19.00 


0.08 


19.00 


0.17 


19.00 


0.25 


19 


20 
21 


20.00 


0.09 


20.00 


0.17 


20.00 


0.26 


20 
21 


21.00 


0.09 


21.00 


0.18 


21.00 


0.27 


22 


22.00 


0.10 


22.00 


0.19 


22.00 


0.29 


22 


23 


23.00 


0.10 


23.00 


0.20 


23.00 


0.30 


23 


24 


24.00 


0.10 


24.00 


0.21 


24.00 


0.31 


24 


25 


25.00 


0.11 


25.00 


0.22 


25.00 


0.33 


25 


26 


26.00 


0.11 


26.00 


0.23 


26.00 


0.34 


26 


27 


27.00 


0.12 


27.00 


0.24 


27.00 


0.35 


27 


28 


28.00 


0.12 


28.00 


0.24 


28.00 


0.37 


28 


29 


29.00 


0.13 


29.00 


0.25 


29.00 


0.38 


29 


30 
31 


30.00 


0.13 


30.00 


0.26 


30.00 


0.39 


30 
31 


31.00 


0.14 


31.00 


0.27 


31.00 


0.41 


32 


32.00 


0.14 


32.00 


0.28 


32.00 


0.42 


32 


33 


33.00 


0.14 


33.00 


0.29 


33.00 


0.43 


33 


34 


34.00 


0.15 


34.00 


0.30 


34.00 


0.45 


34 


35 


35.00 


0.15 


35.00 


0.31 


35.00 


0.46 


35 


36 


36.00 


0.16 


36.00 


0.31 


36.00 


0.47 


36 


37 


37.00 


0.16 


37.00 


0.32 


37.00 


0.48 


37 


38 


38.00 


0.17 


38.00 


0.33 


38.00 


0.50 


38 


39 


39.00 


0.17 


39.00 


0.34 


39.00 


0.51 


39 


40 
41 


40.00 


0.17 


40.00 


0.35 


40.00 


0.52 


40 
41 


41.00 


0.18 


41.00 


0.36 


41.00 


0.54 


42 


42.00 


0.18 


42.00 


0.37 


42.00 


0.55 


42 


43 


43.00 


0.19 


43.00 


0.38 


43.00 


0.56 


43 


44 


44.00 


0.19 


44.00 


0.38 


44.00 


0.58 


44 


45 


45.00 


0.20 


45.00 


0.39 


45.00 


0.59 


45 


46 


46.00 


0.20 


46.00 


0.40 


46.00 


0.60 


46 


47 


47.00 


0.21 


47.00 


0.41 


47.00 


0.62 


47 


48 


48.00 


0.21 


48.00 


0.42 


48.00 


0.63 


48 


49 


49.00 


0.21 


49.00 


0.43 


49.00 


0.64 


49 


50 


50.00 


0-22 


50.00 


0.44 


50.00 


0.65 


50 

■ 
u 

c 

2 


Dep. 

89| 


Lat. 
Dog. 


Dep. 

894 


Lat. 


Dep. 


Lat. 


R9i 


Dcg. 



TRAVERSE TABLE. 



1 

o 
p 

51 


i Deg. 


£E 


eg- 


1 De ? . 


O 
5- 

sr 

s 
o 
n> i 

51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51.00 


0.22 


51.00 


0.45 


51.00 


0.67 


52 


52.00 


0.23 


52.00 


0.45 


52.00 


0.68 


52 


53 


53.00 


0.23 


53.00 


0.46 


53.00 


0.69 


53 


54 


54.00 


0.24 


54.00 


0.47 


54.00 


0.71 


54 


55 


55.00 


0.24 


55.00 


0.48 


55.00 


0.72 


55 


56 


56.00 


0.24 


56.00 


0.49 


56.00 


0.73 


56 


57 


57.00 


0.25 


57.00 


0.50 


57.00 


0.75 


57 


58 


58.00 


0.25 


58.00 


0.51 


57.99 


0.76 


58 


59 


59.00 


0.26 


59.00 


0.51 


58.99 


0.77 


59 


60 
61 


60.00 


0.26 


60.00 


0.52 


59.99 


0.79 


60 
61 


61.00 


0.27 


61.00 


0.53 


60.99 


0.80 


62 


62.00 


0.27 


62.00 


0.54 


61.99 


0.81 


62 


63 


63.00 


0.27 


63.00 


0.55 


62.99 


0.82 


63 


64 


64.00 


0.28 


64.00 


0.56 


63.99 


0.84 


64 


65 


65.00 


0.28 


65.00 


0.57 


64.99 


0.85 


65 


66 


66.00 


0.29 


66.00 


0.58 


65.99 


0.86 


66 


67 


67.00 


0.29 


67.00 


0.58 


66.99 


0.88 


67 


68 


68.00 


0.30 


68.00 


0.59 


67.99 


0.89 


68 


69 


69.00 


0.30 


69.00 


0.60 


68.99 


0.90 


69 


70 
71 


70.00 


0.31 


70.00 


0.61 


69.99 


0.92 


70 
71 


71.00 


0.31 


71.00 


0.62 


70.99 


0.93 


72 


72.00 


0.31 


72.00 


0.63 


71.99 


0.94 


72 


73 


73.00 


0.32 


73.00 


0.64 


72.99 


0.96 


73 


74 


74.00 


0.32 


74.00 


0.65 


73.99 


0.97 


74 


75 


75.00 


0.33 


75.00 


0.65 


74.99 


0.98 


75 


76 


76.00 


0.33 


76.00 


0.66 


75.99 


0.99 


76 


77 


77.00 


0.34 


77.00 


0.67 


76.99 


1.01 


77 ' 


78 


78.00 


0.34 


78.00 


0.68 


77.99 


1.02 


78 i 


79 


79.00 


0.34 


79.00 


0.69 


78.99 


1.03 


79 


80 
81 


80.00 


0.35 


80.00 


0.70 


79.99 


1.05 


80 


81.00 


0.35 


81.00 


0.71 


80.99 


1.06 


81 


82 


82.00 


0.36 


82.00 


0.72 


81.99 


1.07 


82 


83 


83.00 


0.36 


83.00 


0.72 


82.99 


1.09 


83 


84 


84.00 


0.37 


84.00 


0.73 


83.99 


1.10 


84 


85 


85.00 


0.37 


85.00 


0.74 


84.99 


1.11 


85 


86 


86.00 


0.38 


86.00 


0.75 


85.99 


1.13 


86 


87 


87.00 


0.38 


87.00 


0.76 


86.99 


1.14 


87 


88 


88.00 


0.38 


88.00 


0.77 


87.99 


1.15 


88 


89 


89.00 


0.39 


89.00 


0.78 


88.99 


1.16 


89 


90 
91 


90.00 


0.39 


90.00 


0.79 


89.99 


1.18 
1.19 


90 
91 


91.00 


0.40 


91.00 


0.79 


90.99 


92 


92.00 


0.40 


92.00 


0.80 


91.99 


1.20 


92 


93 


93.00 


0.41 


93.00 


0.81 


92.99 


1.22 


93 


94 


94.00 


0.41 


94.00 


0.82 


93.99 


1.23 


94 


95 


95.00 


0.41 


95.00 


0.83 


94.99 


1.24 


95 


96 


96.00 


0.42 


96.00 


0.84 


95.99 


1.26 


96 


97 


97.00 


0.42 


97.00 


0.85 


96.99 


1.27 


97 


98 


98.00 


0.43 


98.00 


0.86 


97.99 


1.28 


98 


99 


99.00 


0.43 


99.00 


0.86 


98.99 


1.30 


99 


100 

o 

1 
s 


100.00 


0.44 


100.00 


0.87 


99.99 


1.31 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


O 

a 

3 


89| 


Deg. 


89i 


Deg. 


893 De~. 



TRAVERSE TABLE. 



■ 

f 

a 
? 


1 Deg. 


H Deg. 


H Deg. 


11 Deg. 


d 

a 
o 
» 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


1.00 


0.02 


1.00 


0.02 


1.00 


0.03 


1.00 


0.03 


1 


2 


2.00 


0.03 


2.00 


0.04 


2.00 


0.05 


2.00 


0.06 


2 


3 


3.00 


0.05 


3.00 


0.07 


3.00 


0.08 


3.00 


0.09 


3 


4 


4.00 


0.07 


4.00 


0.09 


4.00 


0.10 


4.00 


0.12 


4 


5 


5.00 


0.09 


5.00 


0.11 


5.00 


0.13 


5.00 


0.15 


5 


6 


6.00 


0.10 


6.00 


0.13 


6.00 


0.16 


6.00 


0.18 


6 


7 


7.00 


0.12 


7.00 


0.15 


7.00 


0.18 


7.00 


0.21 


7 


8 


8.00 


0.14 


8.00 


0.17 


8.00 


0.21 


8.00 


0.25 


8 


9 


9.00 


0.16 


9.00 


0.20 


9.00 


0.24 


9.00 


0.28 


9 


10 


10.00 


0.17 


10.00 


0.22 


10.00 


0.26 


10.00 


0.31 


10 


11 


11.00 


0.19 


11.00 


0.24 


11.00 


0.28 


10.99 


0.34 


11 


12 


12.00 


0.21 


12.00 


0.26 


12.00 


0.31 


11.99 


0.37 


12 


13 


13.00 


0.23 


13.00 


0.28 


13.00 


0.34 


12.99 


0.40 


13 


14 


14.00 


0.24 


14.00 


0.31 


14.00 


0.37 


13.99 


0.43 


(4 


15 


15.00 


0.26 


15.00 


0.33 


14.99 


0.39 


14.99 


0.46 


15 


16 


16.00 


0.28 


16.00 


0.35 


15.99 


0.42 


15.99 


0.49 


16 


17 


17.00 


0.30 


17.00 


0.37 


16.99 


0.45 


16.99 


0.52 


17 


18 


18.00 


0.31 


18.00 


0.39 


17.99 


0.47 


17.99 


0.55 


18 


19 


19.00 


0.33 


19.00 


0.41 


18.99 


0.50 


18.99 


0.58 


19 


20 


20.00 


0.35 


20.00 


0.44 


19.99 


0.52 


19.99 


0.61 


20 


21 


21.00 


0.37 


21.00 


0.46 


20.99 


0.55 


20.99 


0.64 


21 


22 


22.00 


0.38 


21.99 


0.48 


21,99 


0.58 


21.99 


0.67 


22 


23 


23.00 


0.40 


22.99 


0.50 


22.99 


0.60 


22.99 


0.70 


. 23 


24 


24,00 


0.42 


23.99 


0.52 


23.99 


0.63 


23.99 


0.73 


24 


25 


25.00 


0.44 


24.99 


0.55 


24.99 


0.65 


24.99 


0.76 


25 


26 


26.00 


0.45 


25.99 


0.57 


25.99 


0.68 


25.99 


0.79 


26 


27 


27.00 


0.47 


26.99 


0.59 


26.99 


0.71 


26.99 


0.83 


27 


28 


28.00 


0.49 


27.99 


0.61 


27.99 


0.73 


27.99 


0.86 


28 


29 


29.00 


0.51 


28.99 


0.63 


28.99 


0.76 


28.99 


0.89 


29 


30 


30.00 


0.52 


29.99 


0.65 


29.99 


0.79 


29.99 


0.92 


30 


31 


31.00 


0.54 


30.99 


0.68 


30.99 


0.81 


30.99 


0.95 


31 


32 


32.00 


0,56 


31.99 


0.70 


31.99 


0.84 


31.99 


0.98 


32 


33 


32.99 


0.58 


32.99 


0.72 


32.99 


0.86 


32.98 


1.01 


33 


34 


33.99 


0.59 


33.99 


0.74 


33.99 


0.89 


33.98 


1.04 


34 


35 


34.99 


0,61 


34.99 


0.76 


34.99 


0.92 


34.98 


1.07 


35 


36 


35.99 


0.63 


35.99 


0.79 


35.99 


0.94 


35.98 


1.10 


36 


37 


36.99 


0.65 


36.99 


0.81 


36.99 


0.97 


36.98 


1.13 


37 


38 


37.99 


0.66 


37.99 


0.83 


37.99 


0.99 


37.98 


1.16 


38 


39 


38.99 


0.68 


38.99 


0.85 


38.99 


1.02 


38.98 


1.19 


39 


40 


39.99 


0.70 


39.99 


0.87 


39.99 


1.05 


39.98 


1.22 


40 


41 


40.99 


0.72 


40.99 


0.89 


40.99 


1.07 


40.98 


1.25 


41 


42 


41.99 


0.73 


41.99 


0.92 


41.99 


1.10 


41.98 


1.28 


42 


43 


42.99 


0.75 


42.99 


0.94 


42.99 


1.13 


42.98 


1.31 


43 


44 


43.99 


0.77 


43.99 


0.96 


43.99 


1.15 


43.98 


1.34 


44 


45 


44.99 


0.79 


44.99 


0.98 


44.99 


1.18 


44.98 


1.37 


45 


46 


45.99 


0.80 


45.99 


1.00 


45.99 


1.20 


45.98 


1.40 


46 


47 


46.99 


0.82 


46.99 


1.03 


46.99 


1.23 


46.98 


1.44 


47 


48 


47.99 


0.84 


47.99 


1.05 


47.98 


1.26 


47.98 


1.47 


48 


49 


48.99 


0.86 


48.99 


1.07 


48.98 


1.28 


48.98 


1.50 


49 


50 

■ 
a 

a 

1 

Q 


49.99 


0.87 


49.99 


1.09 


49.98 


1.31 


49.98 


1.53 


50 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


£ 

c 


89] 


Deg. 


88} Deg. 


884 


Deg. 


881 


Deg. 



TRAVERSE TABLE. 



o 

1 

o 
? 


IDeg. 


1 


li Deg. 


H Deg. 


P. 

1 
o 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 ! 50.99 


0.89 


50.99 


1.11 


50.98 


1.34 


50.98 


1.56 


51 


52 , 51.99 


0.91 


51.99 


1.13 


51.98 


1.36 


51.98 


1.59 


52 


53 : 52.99 


0.92 


52.99 


1.16 


52.98 


1.39 


52.98 


1.62 


53 


54 ! 53.99 


0.94 


53.99 


1.18 


53.98 


1.41 


53.97 


1.65 


54 


55 i 54.99 


0.96 


54.99 


1.20 


54.98 


1.44 


54.97 


1.68 


55 


56 ', 55,99 


0.98 


55.99 


1.22 


55.98 


1.47 


55.97 


1.71 


56 


57 ! 56.99 


0.99 


56.99 


1.24 


56.98 


1.49 


56.97 


1.74 


57 


58 ■ 57.99 


1.01 


57.99 


1.27 


57.98 


1.52 


57.97 


1.77 


58 


59 : 58.99 


1.03 


58.99 


1.29 


58.98 


1.54 


58.97 


1.80 


59 


60 ; 59.99 

* 


1.05 


59.99 


1.31 


59.98 


1.57 


59.97 


1.83 


60 


61 i 60.99 


1.06 


60.99 


1.33 


60.98 


1.60 


60.97 


1.86 


61 


62 ; 61.99 


1.08 


61.99 


1.35 


61.98 


1.62 


61.97 


1.89 


62 


63 : 62.99 


1.10 i 


62.99 


1.37 


62.98 


1.65 


62.97 


1.92 


63 


64 ' 63.99 


1.12 


63.98 


1.40 


63.98 


1.68 


63.97 


1.95 


64 


65 1 64.99 


1.13 


| 64.98 


1.42 


64.98 


1.70 


64.97 


1.99 


65 


66 ! 65.99 


1.15 


J 65.98 


1.44 


65.98 


1.73 


65.97 


2.02 


66 


67 1 66.99 


1.17 


66.98 


1.46 


66.98 


1.75 


66.97 


2.05 


67 


68 i 67.99 


1.19 


67.98 


1.48 


67.98 


1.78 


67.97 


2.08 


68 


69 68.99 


1.20 


68.98 


1.51 


68.98 


1.81 


68.97 


2.11 


69 


70 j 69.99 


1.22 


69.98 


1.53 


69.98 


1.83 


69.97 


2.14 


70 


71 70.99 


1.24 


70.98 


1.55 


70.98 


1.86 


70.97 


2.17 


71 


72 


71.99 


1.26 


71.98 


1.57 


71.98 


1.88 


71.97 


2.20 


72 


73 


72.99 


1.27 


72.98 


1.59 


72.97 


1.91 


72.97 


2.23 


73 


74 


73.99 


1.29 


73.98 


1.61 


73.97 


1.94 


73.97 


2.26 


74 


75 


74.99 


1.31 


74.98 


1.64 


74.97 


1.96 


74.97 


2.29 


75 


76 


75.99 


1.33 


75.98 


1.66 


75.97 


1.99 


75.96 


2.32 


76 


77 


76.99 


1.34 


76.98 


1.68 


76.97 


2.02 


76.96 


2.35 


77 


78 


77.99 


1.36 


77.98 


1.70 


77.97 


2.04 


77.96 


2.38 


78 


79 


78.99 


1.38 


78.98 


1.72 


78.97 


2.07 


78.96 


2.41 


79 


80 


79.99 


1.40 


79.98 


1.75 


79.97 


2.09 


79.96 


2.44 


80 


81 j 80.99 


1.41 


80.98 


1.77 


80.97 


2.12 


80.96 


2.47 


81 


82 81.99 


1.43 


81.98 


1.79 


81.97 


2.15 


81.96 


2.50 


82 


83 82.99 


1.45 


82.98 


1.81 


82.97 


2.17 


82.96 


2.53 


83 


84 ' 83.99 


1.47 


83.98 


1.83 


83.97 


2.20 


83.96 


2.57 


84 


85 ! 84.99 


1.48 


84.98 


1.85 


84.97 


2.23 


84.98 


2.60 


85 


86 j 85.99 


1.50 


85.98 


1.88 


85.97 


2.25 


85.96 


2.63 


86 


87 i 86.99 


1.52 


86.98 


1.90 


86.97 


2.28 


86.96 


2.66 


87 


88 1 87.99 


1.54 


87.98 


1.92 


87.97 


2.30 


87.96 


2.69 


88 


89 ' 88.99 


1.55 


88.98 


1.94 


88.97 


2.33 


88.96 


2.72 


89 


90 j 89.99 


1.57 


89.98 


1.96 


89.97 


2.36 


89.96 


2.75 


90 


91 i 90.99 


1.59 


90.98 


1.99 


90.97 


2.38 


90.96 


2.78 


91 


92 ■ 91.99 


1.61 


91.98 


2.01 


91.97 


2.41 


91.96 


2.81 


92 


93 i 92.99 


1.62 


92.98 


2.03 


92.97 


2.43 


92.96 


2.84 


93 ' 


94 ! 93.99 


1.64 


93.98 


2.05 


93.97 


2.46 


93.96 


2.87 


94 


95 J 94.99 


1.66 


• 94.98 


2.07 


94.97 


2.49 


94.96 


2.90 


95 


96 | 95.99 


1.68 


95.98 


2.09 


95.97 


2.51 


95.96 


2.94 


96 


97 9€.99 


1.69 


| 96.98 


2.12 


96.97 


2.54 


96.95 


2.96 


97 


98 


97.99 


1.71 


: 97.98 


2.14 


97.97 


2.57 


97.95 


2.99 


98 


99 


98.98 


1.73 


98.98 


2.16 


98.97 


2.59 


98.95 


3.02 


99 


100 


99.98 


1.75 


99.98 


2.18 


99.97 


2.62 


99.95 


3.05 


100 


o 

a 
5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 
e 
iS 

1 


89 1 


)eg. 


88| Deg. 


88* Deg. 


884 Deg. 



TRAVERSE TABLE. 



g 

1 

a 
? 


2Deg. 


2i Deg. 


2i Deg. 


2| Deg. 


S 

V 

a 

r> 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


1.00 


0.03 


1.00 


0.04 


1.00 


0.04 


1.00 


0.05 


1 


2 


2.00 


0.07 


2.00 


0.08 


2.00 


0.09 


2.00 


0.10 


2 


3 


3.00 


0.10 


3.00 


0.12 


3.00 


0.13 


3.00 


0.14 


3 


4 


4.00 


0.14 


4.00 


0.16 


4.00 


0.17 


4.00 


0.19 


4 


5 


5.00 


0.17 


5.00 


0.20 


5.00 


0.22 


4.99 


0.24 


5 


6 


6.00 


0.21 


6.00 


0.24 


5.99 


0.26 


5.99 


0.29 


6 


7 


7.00 


0.24 


6.99 


0.27 


6.99 


0.31 


6.99 


0.34 


7 


« 


7.99 


0.28 


7.99 


0.31 


7.99 


0.35 


7.99 


0.38 


8 


9 


8.99 


0.31 


8.99 


0.35 


8.99 


0.39 


8.99 


0.43 


9 


10 
11 


9.99 


0.35 


9.99 


0.39 


9.99 


0.44 


9.99 


0.48 


10 


10.99 


0.38 


10.99 


0.43 


10.99 


0.43 


10.99 


0.53 


11 


12 


11.99 


0.42 


11.99 


0.47 


11.99 


0.52 


11.99 


0.58 


12 


13 


12.99 


0.45 


12.99 


0.51 


12.99 


0.57 


12.99 


0.62 


13 


14 


13.99 


0.49 


13.99 


0.55 


13.99 


0.61 


13.98 


0.67 


14 


15 


14.99 


0.52 


14.99 


0.59 


14.99 


0.65 


14.98 


0.72 


15 


16 


15.99 


0.56 


15.99 


0.63 


15.99 


0.70 


15.93 


0.77 


16 


17 


16.99 


0.59 


16.99 


0.67 


16.93 


0.74 


16.98 


0.82 


17 


18 


17.99 


0.63 


17.99 


0.71 


17.98 


0.79 


17.93 


0.86 


18 


19 


18.99 


0.66 


18.99 


0.75 


18.98 


0.83 


18.98 


0.91 


19 


20 


19.99 


0.70 


19.98 


0.79 


19.98 


0.87 


19.98 


0.96 


20 


21 


20.99 


0.73 


20.98 


0.82 


20.98 


0.92 


20.98 


1.01 


21 


22 


21.99 


0.77 


21.98 


0.86 


21.93 


0.96 


21.97 


1.06 


22 


23 


22.99 


0.80 


22.98 


0.90 


22.98 


1.00 


22.97 


1.10 


23 


24 


23.99 


0.84 


23.98 


0.94 


23.98 


1.05 


23.97 


1.15 


24 


25 


24.98 


0.87 


24.98 


0.98 


24.98 


1.09 


24.97 


1.20 


25 


26 


25.98 


0.91 


25.98 


1.02 


25.98 


1.13 


25.97 


1.25 


26 


27 


26.98 


0.94 


26.98 


1.06 


26.97 


1.18 


26.97 


1.30 


27 


23 


27.98 


0.98 


27.98 


1.10 


27.97 


1.22 


27.97 


1.34 


28 


29 


28.98 


1.01 


28.98 


1.14 


28.97 


1.26 


28.97 


1.39 


29 


30 


29.98 


1.05 


29.98 


1.18 


29.97 


1.31 


29.97 


1.44 


30 


31 


30.98 


1.08 


30.98 


1.22 


30.97 


1.35 


30.96 


1.49 


31 


32 


31.98 


1.12 


31.98 


1.26 


31.97 


1.40 


31.96 


1.54 


32 


33 


32.98 


1.15 


32.97 


1.30 


32.97 


1.44 


32.96 


1.58 


33 


34 


33.98 


1.19 


33.97 


1.33 


33.97 


1.48 


33.96 


1.63 


34 


35 


34.98 


1.22 


34.97 


1.37 


34.97 


1.53 


34.96 


1.68 


35 


36 


35.98 


1.26 


35.97 


1.41 


35.97 


1.57 


35.96 


1.73 


36 


37 


36.98 


1.29 


36.97 


1.45 


36.96 


1.61 


36.96 


1.78 


37 


38 


37.98 


1.33 


37.97 


1.49 


37.96 


1.66 


37.96 


1.82 


38 


39 


38.98 


1.36 


38.97 


1.53 


38.96 


1.70 


38.96 


1.87 


39 


; 40 


39.98 


1.40 


39.97 


1.57 


39.96 


1.75 


39.95 


1.92 


40 


41 


40.98 


1.43 


40.97 


1.61 


40.96 


1.77 


40.95 


1.97 


41 


42 


41.97 


1.47 


41.97 


1.65 


41.96 


1.83 


41.95 


2.02 


42 


43 


42.97 


1.50 


42.97 


1.69 


42.96 


1.88 


42.95 


2.06 


43 


44 


43.97 


1.54 


43.97 


1.73 


43.96 


1.92 


43.95 


2.11 


44 


45 


44.97 


1.57 


44.97 


1.77 


44.96 


1.96 


44.95 


2.16 


45 


46 


45.97 


1.61 


45.96 


1.81 


45.96 


2.01 


45.95 


2.21 


46 


47 


46.97 


1.64 


46.96 


1.85 


46.96 


2.05 


46.95 


2.25 


47 


48 


47.97 


1.68 


47.96 


1.88 


47.95 


2.09 


47.95 


2.30 


48 


49 


48.97 


1.71 


48.96 


1.92 


48.95 


2.14 


48.94 


2.35 


49 


50 


49.97 


1.74 


49.96 


1.96 


49.95 


2.18 


49.94 


2.40 


50 


V 

o 

c 

1 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


■ 

c 

a 

1 


88 1 


)eg. 


87| Deg. 


87$ 


Deg. 


87* 


Deg. 



TRAVERSE TABLE. 



o 

s 
? 


2 Deg. 


24 Deg. 


2i Deg. 


2| Deg. 


U 

3" 

to 


Lat. 


Dep 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


50.97 


1.78 


50.96 


2.00 


50.95 


2.22 


50.94 


2.45 


51 


52 


51.97 


1.81 


51.96 


2.04 


51.95 


2.27 


51.94 


2.50 


52 


53 


52.97 


1.85 


52.96 


2.08 


52.95 


2.31 


52.94 


2.54 


53 


54 


53.97 


1.88 


53.96 


2.12 


53.95 


2.36 


53.94 


2.59 


54 


55 


54.97 


1.92 


54.96 


2.16 


54.95 


2.40 


54.94 


2.64 


55 


56 


55.97 


1.95 


55.96 


2.20 


55.95 


2.44 


55.94 


2.69 


56 


57 


56.97 


1.99 


56.96 


2.24 


56.95 


2.49 


56.93 


2.73 


57 


58 


57.96 


2-02 


57.96 


2.28 


57.94 


2.53 


57.93 


2.78 


58 


59 


58.96 


2.06 


58.95 


2.32 


58.94 


2.57 


58.93 


2.83 


59 


60 


59.96 


2.09 


59.95 


2.36 


59.94 


2.62 


59.93 


2.88 


60 


61 


60.96 


2.13 


60.95 


2.39 


60.94 


2.66 


60.93 


2.93 


61 


62 


61.96 


2.16 


61.95 


2.43 


61.94 


2.70 


61.93 


2.97 


62 


63 


62-96 


2.20 


62.95 


2.47 


62.94 


2.75 


62.93 


3.02 


63 


64 


63.96 


2.23 


63.95 


2.51 


63.94 


2.79 


63.93 


3.07 


64 


65 


64.96 


2.27 


64.95 


2.55 


64.94 


2.84 


64.93 


3.12 


65 


66 


65.96 


2.30 


65.95 


2.59 


65.94 


2.88 


65.92 


3.17 


66 


67 


66.96 


2.34 


66.95 


2.63 


66.94 


2.92 


66.92 


3.21 


67 


68 


67.96 


2.37 


67.95 


2.67 


67.94 


2.97 


67.92 


3.26 


68 


69 


68.96 


2.41 


68.95 


2.71 


68.93 


3.01 


68.92 


3.31 


69 


70 


69.96 


2.44 


69.95 


2.75 


69.93 


3.05 


69.92 


3.36 


70 


71 


70.96 


2.48 


70.95 


2.79 


70.93 


3.10 


70.92 


3.41 


71 


72 


71.96 


2.51 


71.94 


2.83 


71.93 


3.14 


71.92 


3.45 


72 


73 


72.96 


2.55 


72.94 


2.87 


72.93 


3.18 


72.92 


3.50 


73 


74 


73.95 


2.58 


73.94 


2.91 


73.93 


3.23 


73.91 


3.55 


74 


75 


74.95 


2.62 


74.94 


2.94 


74.93 


3.27 


74.91 


3.60 


75 


76 


75.95 


2.65 


75.94 


2.98 


75.93 


3.31 


75.91 


3.65 


76 


77 


76.95 


2.69 


76.94 


3.02 


76.93 


3.36 


76.91 


3.70 


77 


78 


77.95 


2.72 


77.94 


3.06 


77.93 


3.40 


77.91 


3.74 


78 


79 


78.95 


2.76 


78.94 


3.10 


78.92 


3.45 


78.91 


3.79 


79 


80 


79.95 


2.79 


79.94 


3.14 


79.92 


3.49 


79.91 


3.84 


80 


81 


80-95 


2.83 


80.94 


3.18 


80.92 


3.53 


80.91 


3.89 


81 


82 


81.95 


2.86 


81.94 


3.22 


81.92 


3.53 


81.91 


3.93 


82 


83 


82.95 


2.90 


82.94 


3.26 


82.92 


3.62 


82.90 


3.98 


83 


84 


83.95 


2.93 


83.94 


3.30 


83.92 


3.66 


83.90 


4.03 


84 


85 


84.95 


2.97 


84.93 


3.34 


84.92 


3.71 


84.90 


4.08 


85 


86 


85.95 


3.00 


85.93 


3.38 


85.92 


3.75 


85.90 


4.13 


86 


87 


86.95 


3.04 


86.93 


3.42 


86.92 


3.79 


86.90 


4.17 


87 


88 


87.95 


3.07 


87.93 


3.45 


87.92 


3.84 


87.90 


4.22 


88 


89 


88.95 


3.11 


88.93 


3.49 


88.92 


3.88 


88.90 


4.27 


89 


90 


89.95 


3.14 


89.93 


3.53 


89.91 


3.93 


89.90 


4.32 


90 


91 


90.95 


3.18 


90.93 


3.57 


90.91 


3.97 


90.90 


4.37 


91 


92 


91.94 


3.21 


91.93 


3.61 


91.91 


4.01 


91.89 


4.41 


92 


93 


92.94 


3.25 


92.93 


3.65 


92.91 


4.06 


92.89 


4.46 


93 


94 


93.94 


3.28 


93.93 


3.69 


93.91 


4.10 


93.89 


4.51 


94 


95 


94.94 


3.32 


94.93 


3.73 


94.91 


4.14 


94.89 


4.56 


95 


96 


95.94 


3.35 


95.93 


3.77 


95.91 


4.19 


95.89 


4.61 


96 


97 


96.94 


3.39 


96.93 


3.81 


96.91 


4.23 


96.89 


4.65 


97 


98 


97.94 


3.42 


97.92 


3.85 


97.91 


4.27 


97.89 


4.70 


98 


99 


98.94 


3.46 


98.92 


3.89 


98.91 


4.32 


98.89 


4.75 


99 


100 


99.94 


3.49 


99.92 


3.93 


99.91 


4.36 


99.88 


4.80 


100 


a 

c 

S3 
«! 

O 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 

1 

'& 


88 1 


3eg. 


87| Deg. 


87i 


Deg. 


874 Deg. 



TRAVERSE TABLE. 



o 

0) 


3Deg. 


34 De ? . 


3J Deg. 


31 De S . 


8 




a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


1.00 


0.05 


1.00 


0.06 


1.00 


0.06 


1.00 


0.06 


l 




2 


2.00 


0.10 


2.00 


0.11 


2.00 


0.12 


2.00 


0.13 


2 




3 


3.00 


0.16 


3.00 


0.17 


2.99 


0.18 


2.99 


0.20 


3 




4 


3.99 


0.21 


3.99 


0.23 


3.99 


0.24 


3.99 


0.26 


4 




5 


4.99 


0.26 


4.99 


0.28 


4.99 


0.31 


4.99 


0.33 


6 




6 


5.99 


0.31 


5.99 


0.34 


5.99 


0.37 


5.99 


0.39 


6 




7 


6.99 


0.37 


6.99 


0.40 


6.99 


0.43 


6.99 


0.46 


7 




8 


7.99 


0.42 


7.99 


0.45 


7.99 


0.49 


7.98 


0.52 


8 




9 


8.99 


0.47 


8.99 


0.51 


8.98 


0.55 


8.98 


0.59 


9 




10 


9.99 


0.52 


9.98 


0.57 


9.98 


0.61 


9.98 


0.65 


10 




11 


10.98 


0.58 


10.98 


0.62 


10.98 


0.67 


10.98 


0.72 


11 




12 


11.98 


0.63 


11.98 


0.68 


11.98 


0.73 


11.97 


0.78 


12 




13 


12.98 


0.68 


12.98 


0.73 


12.98 


0.79 


12.97 


0.85 


13 




14 


13.98 


0.73 


13.98 


0.79 


13.97 


0.86 


13.97 


0.92 


14 




15 


14.98 


0.79 


14.98 


0.85 


14.97 


0.92 


14.97 


0.98 


15 




16 


15.98 


0.84 


15.97 


0.91 


15.97 


0.98 


15.97 


1.05 


16 




17 


16.98 


0.89 


16.97 


0.96 


16.97 


1.04 


16.96 


1.11 


17 




18 


17.98 


0.94 


17.97 


1.02 


17.97 


1.10 


17.96 


1.18 


18 




19 


18.98 


0.99 


18.97 


1.08 


18.96 


1.16 


18.96 


1.24 


19 




20 


19.97 


1.05 


19.97 


1.13 


19.96 


1.22 


19.96 


1.31 


20 




21 


20.97 


1.10 


20.97 


1.19 


20.96 


1.28 


20.96 


1.37 


21 




22 


21.97 


1.15 


21.96 


1.25 


21.96 


1.34 


21.95 


1.44 


22 




23 


22.97 


1.20 


22.96 


1.30 


22.96 


1.40 


22.95 


1.50 


23 




24 


23.97 


1.26 


23.96 


1.36 


23.96 


1.47 


23.95 


1.57 


24 




25 


24.97 


1.31 


24.96 


1.42 


24.95 


1.53 


24.95 


1.64 


25 




26 


25.96 


1.36 


25.96 


1.47 


25.95 


1.59 


25.94 


1.70 


26 




27 


26.96 


1.41 


26.96 


1.53 


26.95 


1.65 


26.94 


1.77 


27 




28 


27.96 


1.47 


27.95 


1.59 


27.95 


1.71 


27.94 


1.83 


28 




29 


28.96 


1.52 


23.95 


1.64 


28.95 


1.77 


28.94 


1.90 


29 




30 


29.96 


1.57 


29.95 


1.70 


29.94 


1.83 


29.94 


1.96 


30 




31 


30.96 


1.62 


30.95 


1.76 


30.94 


1.89 


30.93 


2.03 


31 




32 


31.96 


1.67 


31.95 


1.81 


31.94 


1.95 


31.93 


2.09 


32 




33 


32.95 


1.73 


32.95 


1.87 


32.94 


2.01 


32.93 


2.16 


33 




34 


33.95 


1.78 


33.95 


1.93 


33.94 


2.08 


33.93 


o 22 


34 




35 


34.95 


1.83 


34.94 


1.98 


34.93 


2.14 


34.92 


2.29 


35 




36 


35.95 


1.88 


35.94 


2.04 


35.93 


2.20 


35.92 


2.35 


36 




37 


36.95 


1.94 


36.94 


2.10 


36.93 


2.26 


36.92 


2.42 


37 




38 


37.95 


1.99 


37.94 


2.15 


37.93 


2.32 


37.92 


2.49 


38 




39 


38.95 


2.04 


38.94 


2.21 


38.93 


2.38 


38.92 


2.55 


39 




40 


39.95 


2.09 


39.94 


2.27 


39.93 


2.44 


39.91 


2.62 


40 




41 


40.94 


2.15 


40.93 


2.32 


40.92 


2.50 


40.91 


2.63 


41 




42 


41.94 


2.20 


41.93 


2.38 


41.92 


2.56 


41.91 


2.75 


42 




43 


42.94 


2.25 


42.93 


2.44 


42.92 


2.63 


42.91 


2.81 


43 




44 


43.94 


2.30 


43.93 


2.49 


43.92 


2.69 


43.91 


2.88 


44 




45 


44.94 


2.36 


44.93 


2.55 


44.92 


2.75 


44.90 


2.94 


45 




46 


45.94 


2.41 


45.93 


2.61 


45.91 


2.81 


45.90 


3.01 


46 




47 


46.94 


2.46 


46.92 


2.66 


46.91 


2.87 


46.90 


3.07 


47 




48 


47.93 


2.51 


47.92 


2.72 


47.91 


2.93 


47.90 


3.14 


48 




49 


48.93 


2.56 


48.92 


2.78 


48.91 


2.99 


43.90 


3.20 


49 




50 


49.93 


2.62 


49.92 


2.83 


49.91 


3.05 


49.89 


3.27 


50 




£ 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

a 

Q 




87 L 


)eg. 


86} 


Deg. j 


86J1 


}eg. 


864 Deg. 





TRAVERSE TABLE. 




TKAVKKSE TALLL. 



o 
n 


4 Deg. 


4} Deg. 


4i Deg. 


4| Deg. 


S 
n 

a 1 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


1.00 


0.07 


1.00 


0.07 


1.00 


0.08 


1.00 


0.08 


1 




2 


2.00 


0.14 


1.99 


0.15 


1.99 


0.16 


1.99 


0.17 


2 




3 


2.99 


0.21 


2.99 


0.22 


2.99 


0.24 


2.99 


0.25 


3 




4 


3.99 


0.23 


3.99 


0.30 


3.99 


0.31 


3.98 


0.33 


4 




5 


4.99 


0.35 


4.99 


0.37 


4.98 


0.39 


4.98 


0.41 


5 




6 


5.99 


0.42 


5.98 


0.44 


5.98 


0.47 


5.98 


0.50 


6 




7 


6.98 


0.49 


6.98 


0.52 


6.98 


0.55 


6.97 


0.58 






8 


7.98 


0.56 


7.98 


0.59 


7.98 


0.63 


7.97 


0.66 


8 




9 


8.98 


0.63 


8.98 


0.67 


8.97 


0.71 


8.97 


0.75 







10 


9.98 


0.70 


9.97 


0.74 


9.97 


0.78 


9.97 


0.83 


Hi 




11 


10.97 


0.77 


10.97 


0.82 


10.97 


0.86 


10.96 


091 


11 




12 


11.97 


0.84 


11.97 


0.89 


11.96 


0.94 


11.96 


0.99 


12 




13 


12.97 


0.91 


12.96 


0.96 


12.96 


1.02 


12.96 


1.08 


13 




14 


13.97 


0.98 


13.96 


1.04 


13.96 


1.10 


13.95 


1.16 


14 




15 


14.96 


1.05 


14.96 


1.11 


14.95 


1.18 


14.95 


1-24 


15 




16 


15.96 


1.12 


15.96 


1.19 


15.95 


1.26 


15.95 


1.32 


16 




17 


16.96 


1.19 


16.95 


1.26 


16.95 


1.33 


16.94 


1.41 


17 




18 


17.96 


1.26 


17.95 


1.33 


17.94 


1.41 


17.94 


1.49 


18 




19 


18.95 


1.33 


13.95 


1.40 


18.94 


1.49 


in. 93 


1.57 


19 




20 


19.95 


1.40 


19.95 


1.48 


19.94 


1.57 


19.93 


1.66 


20 




21 


20.95 


1.46 


20.94 


1.56 


20.94 


1.65 


20.93 


1.74 


21 




22 


21.95 


1.53 


21.94 


1.63 


21.93 


1.73 


21.92 


1.82 


22 




1 23 


22.94 


1.60 


22.94 


1.70 


22.93 


1.80 


22.92 


1.90 


23 




24 


23.94 


1.67 


23.93 


1.78 


23.93 


1.88 


23.92 


1.99 


24 




25 


24.94 


1.74 


24.93 


1.85 


24.92 


1.96 


24.91 


2.07 


25 




26 


25.94 


1.81 


25-93 


1.93 


25.92 


2.04 


25.91 


2.15 


26 




27 


26.93 


1.88 


26.93 


2.00 


26.92 


2.12 


26.91 


2.24 


27 




28 


27.93 


1.95 


27.92 


2.08 


27.91 


2.20 


27.90 


2.32 


28 




29 


28.93 


2.02 


28.92 


2.15 


28.91 


2.28 


28.90 


2.40 


29 




30 


29.93 


2.09 


29.92 


2.22 


29.91 


2.35 


29.90 


2.48 


30 




31 


30.92 


2.16 


30.91 


2.30 


30.90 


2.43 


30.89 


2.57 


31 




32 


31.92 


2.23 


31.91 


2.37 


31.90 


2.51 


31.89 


2.65 


32 




33 


32.92 


2.30 


32.91 


2.45 


32.90 


2.59 


32.89 


2.73 


33 




34 


33.92 


2.37 


33.91 


2.52 


33.90 


2.67 


33.88 


2.82 


34 




35 


34.91 


2.44 


34.90 


2.59 


34.89 


2.75 


34.88 


2.90 


35 




36 


35.91 


2.51 


35.90 


2.67 


35.89 


2.82 


35.88 


2-98 


36 




3 1 


36.91 


2.58 


36.90 


2.74 


36.89 


2.90 


36.87 


3.06 


37 




38 


37.91 


2.65 


37.90 


2.82 


37.88 


2.98 


37.87 


3.15 


n 




39 


38.90 


2.72 


38.89 


2.89 


38.88 


3.06 


38.87 


3.23 


:)U 




40 


39.90 


2.79 


39.89 


2.96 


39.88 


3.14 


39.86 


3.31 


40 
41 




41 


40.90 


2.86 


40.89 


3.04 


40.87 


3.22 


40.86 


3.40 




42 


41.90 


2.93 


41.88 


3.11 


41.87 


3.30 


41.86 


3.48 


42 




43 


42.90 


3.00 


42.88 


3.19 


42.87 


3.37 


42.85 


3.56 


43 




44 


43.89 


3.07 


43.88 


3.26 


43.86 


3.45 


43.85 


3.64 


44 




45 


44.89 


3.14 


44.88 


3.33 


44.86 


3.53 


44.85 


3.73 


45 




46 


45.89 


3.21 


45.87 


3.41 


45.86 


3.61 


45.84 


3.81 


46 




47 


46.89 


3.28 


46.87 


3.48 


46.86 


3.69 


46.84 


3.89 


47 




48 


47.88 


3.35 


47.87 


3.56 


47.85 


3.77 


47.84 


3.97 


48 




49 


48.88 


3.42 


48.87 


3.63 


48.85 


3.84 


48.83 


4.06 


49 




50 


49.88 


3.49 


49.86 


3.71 


49.85 


3.92 


49.83 


4.14 


50 




o 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 

a 
$ 

Q 




86 Deg. 


85$ Deg. 


85* 


Deg. 


85i Deg. 





TRAVERSE TABLE. 



11 





g 

1 

o 


4 Deg. 


4| Deg. 


44 Deg. 


42 Deg. 


O 

5" 

CD 








Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




51 


50,83 


3.56 


50.86 


3.78 


50.84 


4.00 


50.82 


4.22 


51 I 




52 


51.87 


3.63 


51.86 


3.85 


51.84 


4.08 


51.82 


4.31 


52 1 




53 


52.87 


3.70 


52.85 


3.93 


52.84 


4.16 


52.82 


4.39 


53 




54 


53.87 


3.77 


53.85 


4.00 


53.83 


4.24 


53.81 


4.47 


54 




55 


54.87 


3.84 


54.85 


4.08 


54.83 


4.32 


54.81 


4.55 


55 ; 




56 


55.86 


3.91 


55.85 


4.15 


55.83 


4.39 


55.81 


4.64 


56 




57 


56.86 


3.98 


56.84 


4.22 


56,82 


4.47 


56.80 


4.72 


57 ; 




58 


57.86 


4.05 


57.84 


4.30 


57.82 


4.55 


57.80 


4.80 


58 


. 


59 


58.86 


4.12 


58.84 


4.37 


58.82 


4.63 


58.80 


4.89 


59 


j 


60 


59.85 


4.19 


59.84 


4.45 


59.82 


4.71 


59.79 


4.97 


60 




61 


60.85 


4.26 


60.83 


4.52 


60.81 


4.79 


60.79 


5.05 


61 




62 


61.85 


4.32 


61.83 


4.59 


61.81 


4.86 


61.79 


5.13 


62 




63 


62,85 


4.39 


62.83 


4.67 


62.81 


4.94 


62.78 


5.22 


63 




64 


63,84 


4.46 


63.82 


4.74 


63-80 


.5.02 


63.78 


5.30 


64 




65 


64.84 


4.53 


64.82 


4.82 


64. GO 


5.10 


64.78 


5.38 


65 




66 


65,84 


4.60 


65-82 


4.89 


65.80 


5.18 


65.77 


5.47 


66 




67 


66.84 


4.67 


66.82 


4.97 


66.79 


5.26 


66.77 


5. .55 


67 • 


■ 


68 


67.83 


4.74 


67.81 


5.04 


67.79 


5.34 


67.77 


5.63 


63 




69 


68.83 


4.81 


68.81 


5.11 


68.79 


5.41 


68.76 


5.71 


69 : 


70 


69.83 


4.88 


69.81 


5.19 


69.78 


5.49 


69.76 


5.80 


70 




71 


70.83 


4.95 


70.80 


5.26 


70.78 


5.57 


70.76 


5.88 


71 : 


| 


72 


71.82 


5.02 


71.80 


5.34 


71.78 


5.65 


71.75 


5.96 


72 


'< 


73 


72.82 


5.09 


72.80 


5.41 


72.77 


5.73 


72.75 


6.04 


73 


74 


73.82 


5.16 


73.80 


5.48 


73.77 


5.81 


73.75 


6.13 


74 ; 


75 


74.82 


5.23 


74.79 


5.56 


74.77 


5.88 


74.74 


6.21 


75 




76 


75.81 


5.30 


75.79 


5.63 


75.77 


5.96 


75.74 


6.29 


76 - 


'; 


77 


76.81 


5.37 


76.79 


5.71 


76.76 


6.04 


76.74 


6.38 


77 




78 


77.81 


5.44 


77.79 


5.78 


77.76 


6.12 


77.73 


6.46 


73 ; 




79 


78.81 


5.51 


78.78 


5.85 


78.76 


6.20 


73.73 


6.54 


79 i 


: 


80 


79.81 


5.58 


79.78 


5.93 


79.75 


6.28 


79.73 


6.62 


80 ■ 


f 


81 


86.80 


5.65 


80.78 


6.00 


80.75 


6.36 


80.72 


6.71 


81 : 




82 


81.80 


5.72 


81.78 


6.08 


81.75 


6.43 


81.72 


6.79 


82 




83 


82.80 


5.79 


82.77 


6.15 


82.74 


6.51 


82.71 


6.87 


83 


: 


84 


83.80 


5.86 


83.77 


6.23 


83.74 


6.59 


83.71 


6.96 


84 . 




85 


84.79 


5.93 


84.77 


6.30 


84.74 


6.67 


84.71 


7.04 


85 


''- 


86 


85.79 


6. 06 


85.76 


6.37 


85.73 


6.75 


85.70 


7.12 


86 




87 


86.79 


6.67 


86.76 


6.45 


86.73 


6.83 


86.70 


7.20 


87 




88 


87.79 


6.14 


87.76 


6.52 


87.73 


6.90 


87.70 


7.29 


88 


89 


88.78 


€.21 


88.76 


6.60 


88.73 


6.98 


88.70 


7.37 


89 : 




90 


89.78 


6.28 


89.75 


6.67 


89.72 


7.06 


89.69 


7.45 


90 i 




91 


90.78 


6.35 


90.75 


6.74 


90.72 


7.14 


90.69 


7.54 


91 


\ 


92 


91.78 


6.42 


91.75 


6.82 


91.72 


7.22 


91.68 


7.62 


92 




93 


92.77 


6.49 


92.74 


6.89 


92.71 


7.30 


92.68 


7.70 


93 


, 


94 


93.77 


6.56 


93.74 


6.97 


93.71 


7.38 


93.68 


7.78 


94 




95 


94.77 


6.63 


94.74 


7.04 


94.71 


7.45 


94.67 


7.87 


95 




96 


95.77 


6.76 


95.74 


7.11 


95.70 


7.53 


95.67 


7.95 


96 




97 


96.76 


6.77 


96.73 


7.19 


96.70 


7.61 


96.67 


8.03 


97 




98 


97.76 


6.84 


97.73 


7.26 


97.70 


7.69 


97.66 


8.12 


98 


\ 


99 


98.76 


6.91 


98.73 


7.34 


98.69 


7.77 


98.66 


8.20 


99 




100 


99.76 


6.98 


99.73 


7.41 


99.69 


7.85 


99.66 


8.28 


100 




1 
1 


Dep. 


Lat 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a 

5 








86 ] 


leg. 


85f 


Deg. 


854 


Deg. 


85} 


Deg. 











12 



TRAVERSE TABLE. 



2 

S3" 
p 
o 

(S 


SD 


eg. 


54 Deg. 






a 
? 



? 




5iE 


I 


5$ E 


eg- 




Lat. 


Dep. 




Lat. 


Dep. 


Lat. 


Dep. 




Lat. 


Dep. 




1 


1.00 


0.09 


1.00 


0.09 


1.00 


0.10 


0.99 


0.10 


1 






1.99 


0.17 


1.99 


0.18 


1.99 


0.19 


1.99 


0.20 


'2 




3 


2.99 


0.26 


2.99 


0.27 


2.99 


0.29 


2.98 


0.30 


3 




. 4 


3.98 


0.35 


3.98 


0.37 


3.98 


0.38 


3.98 


0.40 


4 




5 


4.98 


0.44 


4.98 


0.46 


4.98 


0.48 


4.97 


0.50 


5 




• 6 


5.98 


0.52 


5.97 


0.55 


5.97 


0.58 


5.97 


0.60 


6 




; 7 


6.97 


0.61 


6.97 


0.64 


6.97 


0.67 


6.96 


0.70 


7 




8 


7.97 


0.70 


7.97 


0.73 


7.96 


0.76 


7.96 


0.80 


8 




9 


8.97 


0.78 


8.96 


0.82 


8.96 


0.86 | 


8.95 


0.90 


9 




10 


9.96 


0.87 


9.96 


0.92 


9.95 


0.96 j 


9.95 


1.00 


10 




11 


10.96 


0.96 


10.95 


1.01 


10.95 


1.05 | 


10.94 


1.10 


11 




12 


11.95 


1.05 


11.95 


1.10 


11.94 


1.15 


11.94 


1.20 


12 




. 13 


12.95 


1.13 


12.95 


1.19 


12.94 


1.25 


12.93 


1.30 


13 




14 


13.95 


1.22 


13.94 


1.28 


13.94 


1.34 1 


13.93 


1.40 


14 




15 


14.94 


1.31 


14.94 


1.37 


14.93 


1.44 


14.92 


1.50 


15 




16 


15.94 


1.39 


15.93 


1.46 


15.93 


1.53 


15.92 


1.60 


16 




: 17 


16.94 


1.48 


16.93 


1.56 


16.92 


1.63 


16.91 


1.70 


17 




; 18 


17.93 


1.57 


17.92 


1.65 


17.92 


1.73 


17.91 


1.80 


18 




• 19 


18.93 


1.66 


18.92 


1.74 


18.91 


1.82 


18.90 


1.90 


19 




20 


19.92 


1.74 


19.92 


1.83 


19.91 


1.92 


19.90 


2.00 


20 




21 


20.92 


1.83 


20.91 


1.92 


20.90 


2.01 




2.10 


21 




20.89 




22 


21.92 


1.92 


21.91 


2.01 


21.90 


2.11 


21.89 


2.20 


22 




23 


22.91 


2.00 


22.90 


2.10 


22.89 


2.20 


22.88 


2.30 


23 




. 24 


23.91 


2.09 


23.90 


2.20 


23.89 


2.30 


23.88 


2.40 


24 




• 25 


24.90 


2.18 


24.90 


2.29 


24.88 


2.40 


24.87 


2.50 


25 




26 


25.90 


2.27 


25.89 


2.38 


25.88 


2.49 


25.87 


2.60 


26 




" 27 


26.90 


2.35 


26.89 


2.47 


26.88 


2.59 


26.86 


2.71 


27 




28 


27.89 


2.44 


27.88 


2.56 


27.87 


2.68 


27.86 


2.81 


28 




29 


28.89 


2.53 


28.88 


2.65 


28.87 


2.78 


28.85 


2.91 


29 




\ 30 


29.89 


2.61 


29.87 


2.75 


29.86 


2.88 


29.85 


3.01 


30 




31 


30.88 


2.70 


30.87 


2.84 


30.86 


2.97 


30.84 


3.11 


31 




• 32 


31.88 


2.79 


31.87 


2.93 


31.85 


3.07 


31.84 


3.21 


32 




• 33 


32.87 


2.88 


32.86 


3.02 


32.85 


3.16 


32.83 


3.31 


33 




34 


33.87 


2.96 


33.86 


3.11 


33.84 


3.26 


33.83 


3.41 


34 




35 


34.87 


3.05 


34.85 


3.20 


34.84 


3.35 


34.82 


3.51 


35 




36 


35.86 


3.14 


35.85 


3.29 


35.83 


3.45 


35.82 


3.61 


36 




37 


36.86 


3.22 


36.84 


3.39 


36.83 


3.55 


36.81 


3.71 


37 




38 


37.86 


3.31 


37.84 


3.48 


37.83 


3.64 


37.81 


3.81 


38 




39 


38.85 


3.40 


38.84 


3.57 


38.82 


3.74 


38.80 


3.91 


39 




40 


39.85 


3.49 


39.83 


3.66 


39.82 


3.83 


39.80 


4.01 


40 




41 


40.84 


3.57 


40.83 


3.75 


40.81 


3.93 


40.79 


4.11 


41 




' 42 


41.84 


3.66 


41.82 


3.84 


41.81 


4.03 


41.79 


4.21 


42 




43 


42.84 


3.75 


42.82 


3.93 


42.80 


4.12 


42.78 


4.31 


43 




44 


43.83 


3.83 


43.82 


4.03 


43.80 


4.22 


43.78 


4.41 


44 




45 


44.83 


3.92 


44.81 


4.12 


44.79 


4.31 


44.77 


4.51 


45 




46 


45.82 


4.01 


45.81 


4.21 


45.79 


4.41 


45.77 


4.61 


46 




■■ 47 


46.82 


4.10 


46.80 


4.30 


46.78 


4.50 


46.76 


4.71 


47 




48 


47.82 


4.18 


47.80 


4.39 


47.78 


4.60 


47.76 


4.81 


48 




49 


48.81 


4.27 


48.79 


4.48 


48.77 


4.70 


48.75 


4.91 


49 




50 


49.81 


4.36 


49.79 


4.58 


49.77 


4.79 


49.75 


5.01 


50 




o 

a 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


w 

c 

a 








84* 


Deg. 




Deg. 




85 


Deg. 


84* Deg. 


84* 





TRAVERSE TABLE 




M 



TRAVERSE TABLE. 



g 

n 
P 


6 Deg. 




6i Deg. 


6| Deg. 


C 

o 
ft 


64 Deg. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.99 


0.10 


0.99 


0.11 


0.99 


0.11 


0.99 


0.12 


I 




1.99 


0.21 


1.99 


0.22 


1.99 


0.23 


1.99 


0.24 


2 


3 


2.98 


0.31 


2.98 


0.33 


2.98 


0.34 


2.98 


0.35 


3 


4 


3.98 


0.41 


3.98 


0.44 


3.97 


0.45 


3.97 


0.47 


4 


5 


4.97 


0.52 


4.97 


0.54 


4.97 


0.57 


4.97 


0.59 


5 


6 


5.97 


0.63 


5.96 


0.65 


5.96 


0.68 


5.96 


0.71 


6 


7 


6.96 


0.73 


6.96 


0.76 


6.96 


0.79 


6.95 


0.82 


7 


8 


7.96 


0.84 


7.95 


0.87 


7.95 


0.91 


7.94 


0.94 


8. 


9 


8.95 


0.94 


8.95 


0.98 


8.94 


1.02 


8.94 


1.06 


9 


10 


9.95 


1.05 


9.94 


1.09 


9.94 


1.13 


9.93 


1.18 


10 


11 


10.94 


1.15 


10.93 


1.20 


10.93 


1.25 


10.92 


1.29 


11 


12 


11.93 


1.25 


11.93 


1.31 


11.92 


1.36 


11.92 


1.41 


12 


13 


12.93 


1.36 


12.92 


1.42 


12.92 


1.47 


12.91 


1.53 


13 


14 


13.92 


1.46 


13.92 


1.52 


13.91 


1.59 


13.90 


1.65 


14 


15 


14.92 


1.57 


14.91 


1.63 


14.90 


1.70 


14.90 


1.76 


15 


16 


15.91 


1.67 


15.90 


1.74 


15.90 


1.81 


15.89 


1.88 


16 


17 


16.91 


1.78 


16.90 


1.85 


16.89 


1.92 


16.88 


2-00 


17 , 


18 


17.90 


1.88 


17.89 


1.96 


17.88 


2.04 


17.88 


2.12 


18 


19 


18.90 


1.99 


18.89 


2.07 


18.88 


2.15 


18.87 


2.23 


19 


20 


19.89 


2.09 


19.88 


2.18 


19.87 


2.26 


19.86 


2.35 


20 


21 


20.88 


2.20 


20.88 


2.29 


20.87 


2.38 


20.85 


2.47 


21 


22 


21.88 


2.30 


21.87 


2.40 


21.86 


2.49 


21.85 


2.59 


22 


23 


22.87 


2.40 


22.86 


2.50 


22.85 


2.60 


22.84 


2.70 


23 


24 


23.87 


2.51 


23.86 


2.61 


23.85 


2.72 


23.83 


2.82 


24 


25 


24.86 


2.61 


24.85 


2.72 


24.84 


2.83 


24.83 


2.94 


25 


26 


25.86 


2.72 


25.85 


2.83 


25.83 


2.94 


25.82 


3.06 


26 


27 


26.85 


2.82 


26.84 


2.94 


26.83 


3.06 


26.81 


3.17 


27 


28 


27.85 


2.93 


27.83 


3.05 


27.82 


3.. 17 


27.81 


3.29 


28 


29 


28.84 


3.03 


28.83 


3.16 


28.81 


3.28 


28.80 


3.41 


29 


30 


29.84 


3.14 


29.82 


3.27 


29.81 


3.40 


29.79 


3.53 


30 


31 


30.83 


3.24 


30.82 


3.37 


30.80 


3.51 


30.79 


3.64 


31 


32 


31.82 


3.34 


31.81 


3.48 


31.79 


3.62 


31.78 


3.76 


32 


33 


32.82 


3.45 


32.80 


3.59 


32.79 


3.74 


; 32.77 


a. 88 


33 


34 


33.81 


3.55 


33.80 


3.70 


33.78 


3.85 


33.76 


4.00 


34 


35 


34.81 


3.66 


34.79 


3.81 


34.78 


3.96 


34.76 


4.11 


35 


36 


35.80 


3.76 


35.79 


3.92 


35.77 


4.08 


35.75 


4.23 


36 


37 


36.80 


3.87 


36.78 


4.03 


36.76 


4.19 


36.75 


4.35 


37 


38 


37.79 


3.97 


37.77 


4.14 


37.76 


4.30 


37.74 


4.47 


38 ; 


39 


38.79 


4.08 


38.77 


4.25 


38.75 


4.41 


38.73 


4.58 


39 


40 


39.78 


4.18 


39.76 


4.35 


39.74 


4.53 


39.72 


4.70 


40 


41 


40.78 


4.29 


40.76 


4.46 


40.74 


4.64 


40.72 


4.82 


41 


42 


41.77 


4.39 


41.75 


4.57 


41.73 


4.76 


41.71 


4.94 


42 


43 


42.76 


4.49 


42.74 


4.68 


42.72 


4.87 


42.70 


5.05 


43 


44 


43.76 


4.60 


43.74 


4.79 


43.72 


4.98 


43.70 


5.17 


44 


45 


44.75 


4.70 


44.73 


4.90 


44.71 


5.09 


44.69 


5.29 


45 


46 


45.75 


4.81 


45.73 


5.01 


45.70 


5.21 


45.68 


5.41 


46 


47 


46.74 


4.91 


46.72 


5.12 


46.70 


5.32 


46.67 


5.52 


47 


48 


47.74 


5.02 


47.71 


5.23 


47.69 


5.43 


47.67 


5.64 


48 


49 


48.73 


5.12 


48.71 


5.34 


48.69 


5.55 


48.66 


5.76 


49 


50 


49.73 


5.23 


49.70 


5.44 


49.68 


5.66 


49.65 


5.88 


50 


O 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


■ 

1 


.2 


















Q 


84 1 


Deg. 


83| 


Deg. 


83J 


Deg. 


834 


Deg. 


5 



TRAVERSE TABLE. 




16 



TRAVERSE TABLE 



d 

3 

a 
? 


7Deg. 


7i Deg. 


7i Deg. 


7| Deg. 


I 

3 
O 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.99 


0.12 


0.99 


0.13 


0.99 


0.13 


0.99 


0.13 


1 


2 


1.99 


0.24 


1.98 


0.25 


1.98 


0.26 


1.93 


0.27 


2 


3 


2.98 


0.37 


2.98 


0.38 


2.97 


0.39 


2.97 


0.40 


3 


4 


3.97 


0.49 


3.97 


0.50 


3.97 


0.52 


3.96 


0.54 


4 


5 


4.96 


0.61 


4.96 


0.63 


4.96 


0.65 


4.95 


0.67 


5 


6 


5.96 


0.73 


5.95 


0.76 


5.95 


0.78 


5.95 


0.81 


6 


7 


6.95 


0.85 


6.94 


0.88 


6.94 


0.91 


6.94 


0.94 


7 I 


8 


7.94 


0.97 


7.94 


1.01 


7.93 


1.04 


7.93 


1.08 


8 


9 


8.93 


1.10 


8.93 


1.14 


8.92 


1.17 


8.92 


1.21 


9 


10 


9.93 


1.22 


9.92 


1.26 


9.91 


1.31 


9.91 


1.35 


10 


11 


10.92 


1.34 


10.91 


1.39 


10.91 


1.44 


; 10.90 


1.48 


11 


12 


11.91 


1.46 


11.90 


1.51 


11.90 


1.57 


J 11.89 


1.62 


12 


13 


12.90 


1.58 


12.90 


1.64 


12.89 


1.70 


12.88 


1.75 


13 


14 


13.90 


1.71 


13.89 


1.77 


13.88 


1.83 


13.87 


1.89 


14 


15 


14.89 


1.83 


14.88 


1.89 


14.87 


1.96 


14.86 


2.02 


15 


16 


15.88 


1.95 


15.87 


2.02 


15.86 


2.09 


15.85 


2.16 


16 


17 


16.87 


2.07 


16.86 


2.15 


16.85 


2.22 


16.84 


2.29 


17 


18 


17.87 


2.19 


17.86 


2.27 


17.85 


2.35 


17.84 


2.43 


18 


19 


18.86 


2.32 


18.85 


2.40 


18.84 


2.48 


18.83 


2.56 


19 


20 


19.85 


2.44 


19.84 


2.52 


19.83 


2.61 


19.82 


2.70 


20 


21 


20.84 


2.56 


20.83 


2.65 


20.82 


2.74 


20.81 


2.83 


21 


22 


21.84 


2.68 


21.82 


2.78 


21.81 


2.87 


21.80 


2.97 


22 


23 


22.83 


2.80 


22.82 


2.90 


22.80 


3.00 


22.79 


3.10 


23 


24 


23.82 


2.92 


23 81 


3.03 


23.79 


3.13 


23.78 


3.24 


24 


25 


24.81 


3.05 


24.80 


3.15 


24.79 


3.26 


24.77 


3.37 


25 


26 


25.81 


3.17 


25.79 


3.28 


25.78 


3.39 


25.76 


3.51 


26 


27 


26.80 


3.29 


26.78 


3.41 


26.77 


3.52 


26.75 


3.64 


27 


28 


27.79 


3.41 


27.78 


3.53 


27.76 


3.65 


27.74 


3.78 


28 


29 


28.78 


3.53 


28.77 


3.66 


28.75 


3.79 


28.74 


3.91 


29 


30 


29.78 


3.66 


29.76 


3.79 


29.74 


3.92 


29.73 


4.05 


30 


31 


30.77 


3.78 


30. 7> 


3.91 


30.73 


4.05 


30.72 


4.18 


31 


32 


31.76 


3.90 


31.74 


4.04 


31.73 


4.18 


31.71 


4.32 


32 


33 


32.75 


4.02 


32.74 


4.16 


32.72 


4.31 


32.70 


4.45 


33 


34 


33.75 


4.14 


33.73 


4.29 


33.71 


4.44 


33.69 


4.58 


34 


35 


34.74 


4.27 


34.72 


4.42 


34.70 


4.57 


34.68 


4.72 


35 < 


36 


35.73 


4.39 


35.71 


4.54 


35.69 


4.70 


35.67 


4.85 


36 


37 


36.72 


4.51 


36.70 


4.67 


36.68 


4.83 


36.66 


4.99 


37 


38 


37.72 


4.63 


37.70 


4.80 


37.67 


4.96 


37.65 


5.12 


38 


39 


38.71 


4.75 


38.69 


4.92 


38.67 


5.09 


38.64 


5.26 


39 


40 


39.70 


4.87 


39.68 


5.05 


39.66 


5.22 


39.63 


5.39 


40 


41 


40.70 


5.00 


40.67 


5.17 


40.65 


5.35 


I 40.63 


5.53 


41 


42 


41.69 


5.12 


41.66 


5.30 


41.64 


5.48 


: 41.62 


5.66 


42 


43 


42.68 


5.24 


42.66 


5.43 


42.63 


5.61 


| 42.61 


5.80 


43 


44 


43.67 


5.36 


43.65 


5.55 


43.62 


5.74 


! 43.60 


5.93 


44 


45 


44.67 


5.48 


44.64 


5.68 


44.62 


5.87 


44.59 


6.07 


45 


46 


45.66 


5.61 


45.63 


5.81 


45.61 


6.00 


45.58 


6.20 


46 


47 


46.65 


5.73 


46.62 


5.93 


46.60 


6.13 


46.57 


6.34 


47 


48 


47.64 


5.85 


47.62 


6.06 


47.59 


6.27 


47.56 


6.47 


48 


49 


48.63 


5.97 


48.61 


6.18 


48.58 


6.40 


48.55 


6.61 


49 


50 


49.63 


6.09 


49.60 


6.31 


49.57 


6.53 


49.54 


6.74 


50 


gj 
a 


Dep. 


Lat. 


Dep 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


■ 
o 
a 
I 

5 


&°\ T 


„ ? 


<\r?l 


Deg. 


82} Deg. 


82* Deg. 



TRAVERSE TABLE. 



17 





1 

a 
5 
? 


7 Deg. 


7* Deg. 


7i Deg. 


7| Deg. 


g 

ST 

o 

a 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




51 


50.62 


6.22 


50.59 


6.44 


50.56 


6.66 


50.53 


6.88 


51 




52 


51.61 


6.34 


51.58 


6.56 


51.56 


6.79 


51.53 


7.01 


52 




53 


52.60 


6.46 


52.58 


6.69 


52.55 


6.92 


52.52 


7.15 


53 




54 


53.60 


6.58 


53.57 


6.81 


53.54 


7.05 


53.51 


7.28 


54 




55 


54.59 


6.70 


54.56 


6.94 


54.53 


7.18 


54.50 


7.42 


55 




56 


55.58 


6.82 


55.55 


7.07 


55.52 


7.31 


55.49 


7.55 


56 




57 


56.58 


6.95 


56.54 


7.19 


56.51 


7.44 


56.48 


7.69 


57 




58 


57.57 


7.07 


57.54 


7.32 


57.50 


7.57 


57.47 


7.82 


58 




59 


58.56 


7.19 


58.53 


7.45 


58.50 


7.70 


58.46 


7.96 


59 




60 


59.55 


7.31 


59.52 


7.57 


59.49 


7.83 


59.45 


8.09 


60 




61 


60.55 


7.43 


60.51 


7.70 


60.48 


7.96 


60.44 


8.23 


61 




62 


61.54 


7.56 


61.50 


7.82 


61.47 


8.09 


61.43 


8.36 


62 




63 


62.53 


7.68 


62.50 


7.95 


62.46 


8.22 


62.42 


8.50 


63 




64 


63.52 


7.80 


63.49 


8.08 


63.45 


8.35 


63.42 


8.63 


64 




65 


64.52 


7.92 


64.48 


8.20 


64.44 


8.48 


64.41 


8.77 


65 




66 


65.51 


8.04 


65.47 


8.33 


65.44 


8.61 


65.40 


8.90 


66 




67 


66.50 


8.17 


66.46 


8.46 


66.43 


8.75 


66.39 


9.04 


67 




68 


67.49 


8.29 


67.46 


8.58 


67.42 


8.88 


67.38 


9.17 


68 




69 


68.49 


8.41 


68.45 


8.71 


68.41 


9.01 


68.37 


9.30 


69 




70 


69.48 


8.53 


69.44 


8.83 


69.40 


9.14 


69.36 


9.44 


70 




71 


70.47 


8.65 


70.43 


8.96 


70.39 


9.27 


70.35 


9.57 


71 




72 


71.46 


8.77 


71.42 


9.09 


71.38 


9.40 


71.34 


9.71 


72 




73 


72.46 


8.90 


72.42 


9.21 


72.38 


9.53 


72.33 


9.84 


73 , 




74 


73.45 


9.02 


73.41 


9.34 


73.37 


9.66 


73.32 


9.98 


74 




75 


74.44 


9.14 


74.40 


9.46 


74.36 


9.79 


74.31 


10.11 


75 




76 


75.43 


9.26 


75.39 


9.59 


75.35 


9.92 


75.31 


10.25 


76 




77 


76.43 


9.38 


76.38 


9.72 


76.34 


10.05 


76.30 


10.38 


77 




78 


77.42 


9.51 


77.38 


9.84 


77.33 


10.18 


77.29 


10.52 


78 




79 


78.41 


9.63 


78.37 


9.97 


78.32 


10.31 


78.28 


10.65 


79 




80 


79.40 


9.75 


79.36 


10.10 


79.32 


10.44 


79.27 


10.79 


80 




81 


80.40 


9.87 


80.35 


10.22 


80.31 


10.57 


80.26 


10.92 


81 




82 


81.39 


9.99 


81.34 


10.35 


81.30 


10.70 


81.25 


11.06 


82 




83 


82.38 


10.12 


82.34 


10.47 


82.29 


10.83 


82.24 


11.19 


83 




84 


83.37 


10.24 


83.33 


10.60 


83.28 


10.96 


83.23 


11.33 


84 




85 


84.37 


10.36 


84.32 


10.73 


84.27 


11.09 


84.22 


11.46 


85 




86 


85.36 


10.48 


85.31 


10.85 


85.26 


11.23 


85.21 


11.60 


86 




87 


86.35 


10.60 


86.30 


10.98 


86.26 


11.36 


86.21 


11.73 


87 




88 


87.34 


10.72 


87.30 


11.11 


87.25 


11.49 


87.20 


11.87 


88 




89 


88.34 


10.85 


88.29 


11.23 


88.24 


11.62 


88.19 


12.00 


89 


' 


90 


89.33 


10.97 


89.28 


11.36 


89.23 


11.75 


89.18 


12.14 


90 




91 


90.32 


11.09 


90.27 


11.48 


90.22 


11.88 


90.17 


12.27 


91 




92 


91.31 


11.21 


91.26 


11.61 


91.21 


12.01 


91.16 


12.41 


92 




93 


92.31 


11.33 


92.26 


11.74 


92.20 


12.14 


92.15 


12.54 


93 




94 


93.30 


11.46 


93.25 


11.86 


93.20 


12.27 


93.14 


12.68 


94 




95 


94.29 


11.58 


94.24 


11.99 


94.19 


12.40 


94.13 


12.81 


95 




96 


95.28 


11.70 


95.23 


12.12 


95.18 


12.53 


95.12 


12.95 


96 




97 


96.28 


11.82 


96.22 


12.24 


96.17 


12.66 


96.11 


13.08 


97 




98 


97.27 


11.94 


97.22 


12.37 


97.16 


12.79 


97.10 


13.22 


98 




99 


98.26 


12.07 


98.21 


12.49 


98.15 


12.92 


98.10 


13.35 


99 




100 


99.25 


12.19 


99.20 


12.62 


99.14 


13.05 


99.09 


13.49 


100 




«3 
o 

a 

3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a! 

o 
a ■ 

5 




83 1 


)eg. 


82| 


Deg. 


82* 


Deg. ! 


82i 1 


^esr. 



2P 



lb 



TRAVERSE TABLE 



3 

P 

o 
a 


8D 


e S- 


84 Deg. 


8i Deg. 


8$ Deg. 


P 

V 

s 
a 
B 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


0.99 


0.14 


0.99 


0.14 


0.99 


0.15 


0.99 


0.15 


1 




2 


1.98 


0.28 


1.98 


0.29 


1.98 


0.30 i 


1.98 


0.30 


2 




3 


2.97 


0.42 


2.97 


0.43 


2.97 


0.44 i 


2.97 


0.46 


3 




4 


3.96 


0.56 


3.96 


0.57 


3.96 


0.59 ! 


3.95 


0.61 


4 




5 


4.95 


0.70 


4.95 


0.72 


4.95 


0.74 | 


4.94 


0.76 


5 




6 


5.94 


0.84 


5.94 


0.86 


5.93 


0.89 ! 


5.93 


0.91 


6 




7 


6.93 


0.97 


6.93 


1.00 


6.92 


1.03 


6.92 


1.06 


7 




8 


7.92 


1.11 


7.92 


1.15 


7.91 


1.18 


7.91 


1.22 


8 




9 


8.91 


1.25 


8.91 


1.29 


8.90 


1.33 


8.90 


1.37 


9 




10 


9.90 


1.39 


9.90 


1.43 


9.89 


1.48 


9.88 


1.52 


10 




11 


10.89 


1.53 


10.89 


1.58 


10.88 


1.63 


10.87 


1.67 


11 




12 


11.88 


1.67 


11.88 


1.72 


11.87 


1.77 


11.86 


1.83 


12 




13 


12.87 


1.81 


12.87 


1.87 


12.86 


1.92 


12.85 


1.98 


13 




14 


13.86 


1.95 


13.86 


2.01 


13.85 


2.07 


13.84 


2.13 


14 




15 


14.85 


2.09 


14.85 


2.15 


14-84 


2.22 


14.83 


2.28 


15 




16 


15.84 


2.23 


15.84 


2.30 


15.82 


2.36 


15.81 


2.43 


16 




17 


16.83 


2.37 


16.83 


2.44 


16.81 


2.51 


16.80 


2.59 


17 




18 


17.82 


2.51 


17.81 


2.58 


17.80 


2.66 


17.79 


2.74 


18 




19 


18.82 


2.64 


18.80 


2.73 


18.79 


2.81 


18.78 


2.89 


19 




20 


19.81 


2.78 


19.79 


2.87 


19.78 


2.96 


19.77 


3.04 


20 




21 


20.80 


2.92 


20.78 


3.01 


20.77 


3.10 


20.76 


3.19 


21 




22 


21.79 


3.06 


21.77 


3.16 


21.76 


3.25 


21.74 


3.35 


22 




23 


22.78 


3.20 


22.76 


3.30 


22.75 


3.40 


22.73 


3.50 


23 




24 


23.77 


3.34 


23.75 


3.44 


23.74 


3.55 


23.72 


3.65 


24 




25 


24.76 


3.48 


24.74 


3.59 


24.73 


3.70 


24.71 


3-80 


25 




20 


25.75 


3.62 


25.73 


3.73 


25.71 


3.84 


25.70 


3.96 


26 




27 


26.74 


3.76 


26.72 


3.87 


26.70 


3.99 


26.69 


4.11 


27 




28 


27.73 


3.90 


27.71 


4.02 


27.69 


4.14 


27.67 


4.26 


28 




29 


28.72 


4.04 


28.70 


4.16 


28.68 


4.29 


28.66 


4.41 


29 




30 


29.71 


4.18 


29.69 


4.30 


29.67 


4.43 


29.65 


4.56 


30 




31 


30.70 


4.31 


30.68 


4.45 


30.66 


4.58 


30.64 


4.72 


31 




32 


31.69 


4.45 


31.67 


4.59 


31.65 


4.73 


31.63 


4.87 


32 




33 


32.68 


4 59 


32.66 


4.74 


32.64 


4.88 


32.62 


5.02 


33 




34 


33.67 


4.73 


33.65 


4.88 


33.63 


5.03 


33.60 


5.17 


34 




35 


34.66 


4.87 


34.64 


5.02 


34.62 


5.17 


34.59 


5.32 


35 




36 


35.65 


5.01 


35.63 


5.17 


35.60 


5.32 


3.5.58 


5.48 


36 




37 


36.64 


5.15 


36.62 


5.31 


36.59 


5.47 


36.57 


5.63 


37 




38 


37.63 


5.29 


37.61 


5.45 


37.58 


5.62 


37.56 


5.7:: 


38 




39 


38.62 


5.43 


38.60 


5.60 


38.57 


5.76 


38.55 


5.93 


39 




40 


39.61 


5.57 


39.59 


5.74 


39.56 


5.91 


39.53 


6.08 


40 




41 


40.60 


5.71 


40.58 


5.88 


40.55 


6.06 


40.52 


6.24 


41 




42 


41.59 


5.85 


41.57 


6.03 


41.54 


6.21 


41.51 


6.39 


42 




43 


42.58 


5.98 


42.56 


6.17 


42.53 


6.36 


42.50 


6.54 


43 




44 


43.57 


6.12 


43.54 


6.31 


43.52 


6.50 


43.49 


6.69 


44 




45 


44.56 


6.26 


44.53 


6.46 


44.51 


6.65 


44.48 


6.85 


45 




46 


45.55 


6.40 


45.52 


6.60 


45.49 


6.80 


45.46 


7.00 


46 




47 


46.54 


6.54 


46.51 


6.74 


46.48 


6.95 


46.45 


7.15 


47 




48 


47.53 


6.68 


47.50 


6.89 


47.47 


7.09 


47.44 


7.30 


48 




49 


48.52 


6.82 


48.49 


7.03 


48.46 


7.24 


48.43 


7.45 


49 




50 


49.51 


6.96 


49.48 


7.17 


49.45 


7.39 


49.42 


7.61 


50 




Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a 

c 




82 

1 


Deg. 


8U 


Beg. 


81i 


De °- 


8H 


Deg. 





TRAVERSE TABLE. 



19 





o 

o 
? 


8 Deg. 


8i Deg. 


| m Deg. 


8| Deg. 


b 

3 
O 
CD 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




51 


50.50 


7.10 


50.47 


7.32 


50.44 


7.54 


50.41 


7.76 


51 




52 


51.49 


7.24 


51.46 


7.46 


51.43 


7.69 


51.39 


7.91 


52 




53 


52.48 


7.38 


52.45 


7.61 


52.42 


7.83 


52.38 


8.06 


53 




54 


53.47 


7.52 


53.44 


7.75 


53.41 


7.98 


53.37 


8.21 


54 ' 




55 


54.46 


7.65 


54.43 


7.89 


54.40 


8.13 


54.36 


8.37 


55 




56 


55.46 


7.79 


55.42 


8.04 


55.38 


8.28 


55.35 


8.52 


56 




57 


56.45 


7.93 


56.41 


8-18 


56.37 


8.43 


56.34 


8.67 


57 




58 


57.44 


8.07 


57.40 


8.32 


57.36 


8.57 


57.32 


8.82 


58 




59 


58.43 


8.21 


58.39 


8.47 


58.35 


8.72 


58.31 


8.98 


59 




60 


59.42 


8.35 


59.38 


8.61 


59.34 


8.87 


59.30 


9.13 


60 




61 


60.41 


8.49 


60.37 


8.75 


60.33 


9.02 


60.29 


9.28 


61 




62 


61.40 


8.63 


61.36 


8.90 


61.32 


9.16 


61.28 


9.43 


62 




63 


62.39 


8.77 


62.35 


9.04 


62.31 


9.31 


62.27 


9.58 


63 




64 


63.38 


8.91 


63.34 


9.18 


63.30 


9.46 


63.26 


9.74 


64 




65 


64.37 


9.05 


64.33 


9.33 


64.29 


9.61 


64.24 


9.89 


65 




66 


65.36 


9.19 


65.32 


9.47 


65.28 


9.76 


65.23 


10.04 


66 




67 


66.35 


9.32 


66.31 


9.61 


66.26 


9.90 


66.22 


10.19 


67 




68 


67.34 


9.46 


67.30 


9.76 


67.25 


10.05 


67.21 


10.34 


68 




69 i 68.33 


9.60 


68.29 


9.90 


68.24 


10.20 


68.20 


10.50 


69 




70 69.32 


9.74 


69.28 


10.04 


69.23 


10.35 


69.19 


10.65 


70 




71 70.31 


9.88 


70.27 


10.19 


70.22 


10.49 


70.17 


10.80 


71 




72 


71.30 


10.02 


71.25 


10.33 


71.21 


10.64 


71.16 


10.95 


72 




73 


72.29 


10.16 


72.24 


10.47 


72.20 


10.79 


72.15 


11.10 


73 




74 


73.28 


10.30 


73.23 


10.62 


73.19 


10.94 


73.14 


11.26 


74 




75 


74.27 


10.44 


74.22 


10.76 


74.18 


11.09 


74.13 


11.41 


75 




76 


75.26 


10.58 


75.21 


10.91 


75.17 


11.23 


75.12 


11.56 


76 




77 76.25 


10.72 


76.20 


11.05 


76.15 


11.38 


76.10 


11.71 


77 




78 ! 77.24 


10.86 


77.19 


11.19 


77.14 


11.53 


77.09 


11.87 


78 . 




79 1 78.23 


10.99 


78.18 


11.34 


78.13 


11.68 


78.08 


12.02 


79 




80 j 79.22 


11.13 


79.17 


11.48 


79.12 


11.82 


79.07 


12.17 


80 




81 


80.21 


11.27 


80.16 


11.62 


! 80.11 


11.97 


80.06 


12.32 


81 




82 


81.20 


11.41 


81.15 


11.77 


81.10 


12.12 


81.05 


12.47 


82 




83 


82.19 


11.55 


82.14 


11.91 


82.09 


12.27 


82.03 


12.63 


83 




84 


83.18 


11.69 


83.13 


12.05 


83.08 


12.42 


83.02 


12.78 


84 




85 


84.17 


11.83 


84.12 


12.20 


84.07 


12.56 


84.01 


12.93 


85 




86 


85.16 


11.97 


85.11 


12.34 


85.06 


12.71 


85.00 


13.08 


86 




87 


86.15 


12.11 


86.10 


12.48 


86.04 


12.86 


85.99 


13.23 


87 




88 


87.14 


12.25 


87.09 


12.63 


87.03 


13.01 


86.98 


13.39 


88 




89 


88.13 


12.39 


88.08 


12.77 


88.02 


13.16 


87.96 


13.54 


89 




90 


89.12 


12.53 


89.07 


12.91 


89.01 


13.30 


88.95 


13.69 


90 




91 


90.11 


12.66 


90.06 


13.06 


90.00 


13.45 


89.94 


13.84 91 




92 


91.10 


12.80 


91.05 


13.20 


90.99 


13.60 


90.93 


14.00 


92 




93 


92.09 


12.94 


92.04 


13.34 


91.98 


13.75 


91.92 


14.15 


93 




94 


93.09 


13.08 


93.03 


13.49 


92.97 


13.89 


92.91 


14.30 


94 




95 


94.08 


13.22 


94.02 


13.63 


93.96 


14.04 


93.89 


14.45 


95 ' 




96 


95.07 


13.36 


95.01 


13.78 


94.95 


14.19 


94.88 


14.60 


96 




97 


96.06 


13.50 


96.00 


13.92 


95.93 


14.34 


95.87 


14.76 


97 




98 


97.05 


13.64 


96.99 


14.06 


96.92 


14.49 


96.86 


14.91 


98 




99 


98.04 


13.78 


97.98 


14.21 


97.91 


14.63 


97.85 


15.06 


99 




100 


99.03 


13.92 


98.97 


14.35 


98.90 


14.78 


98.84 


15.21 


100 




1 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. | 


Lat. 


Dep. 


Lat. 


6 
o 

1 




82 I 


)eg. 


81| Deg. 


81 i Deg. 


814 Deg. 



20 



TrtAVERSE TABLE. 





O 

3 


9Deg. 




94 Deg. 


Q * Deg. 


» 

s 
o 
re 




9i Deg. 




Lat. 


Dep. 


Lat. 


Dep. i 


Lat. 


Dep. 


Lat. 


Dep. 




1 


0.99 


0.16 


0.99 


0.16 


0.99 


0.17 j 


0.99 


0.17 


1 




2 


1.98 


0.31 


1.97 


32 


1.97 


0.33 


1.97 


0.34 


2 




3 


2.96 


0.47 


2.96 


0."*, 


2.96 


0.50 


2.96 


0.51 


3 




4 


3.95 


0.63 


3.95 


0.64 


3.95 


0.66 


3.94 


0.68 


4 




5 


4.94 


0.78 


4.93 


0.80 


4.93 


0.83 


4.93 


0.85 


5 




6 


5.93 


0.94 


5.92 


0.96 


5.92 


0.99 


5.91 


1.02 


fj 




7 


6.91 


1.10 


6.91 


1.13 


6.90 


1.16 


6.90 


1.19 


1 




8 


7.90 


1.25 


7.90 


1.29 


7.89 


1.32 


7.88 


1.35 


8 




9 


8.89 


1.41 


8.88 


1.45 


8.88 


1.49 


8.87 


1.52 


9 




10 
11 


9.88 


1.56 


9.87 


1.61 


9.86 


1.65 


9.86 


1.69 


10 ' 




10.86 


1.72 


10.86 


1.77 


10.85 


1.82 


10.84 


1.86 


11 




12 


11.85 


1.88 


11.84 


1.93 


11.84 


1.98 


11.83 


2.03 


12 




13 


12.84 


2.03 


12.83 


2.09 


12.82 


2.15 


12.81 


2.20 


13 




14 


13.83 


2.19 


13.82 


2.25 


13.81 


2.31 


13.80 


2.37 


14 




15 


14.82 


2.35 


14.80 


2.41 


14.79 


2.48 


14.78 


2.54 


15 




16 


15.80 


2.50 


15.79 


2.57 


15.78 


2.64 


15.77 


2.71 


16 




17 


16.79 


2.66 


16.78 


2.73 


16.77 


2.81 


16.75 


2.88 


17 




18 


17.78 


2.82 


17.77 


2.89 


17.75 


2.97 


17.74 


3.05 


18 ' 




19 


18.77 


2.97 


18.75 


3.05 


18.74 


3.14 


18.73 


3.22 


19 




20 


19.75 


3.13 


19.74 


3.21 


19.73 


3.30 


19.71 


3.39 


20 




21 


20.74 


3.29 


20.73 


3.38 


20.71 


3.47 


20.70 


3.56 


21 




22 


21.73 


3.44 


21.71 


3.54 


21.70 


3.63 


21.68 


3.73 


22 




23 


22.72 


3.60 


22.70 


3.70 


22.68 


3.80 


22.67 


3.90 


23 




24 


23.70 


3.75 


23.69 


3.86 


23.67 


3.96 


23.65 


4.06 


24 




25 


24.69 


3.91 


24.67 


4.02 


24.66 


4.13 


24.64 


4.23 


25 




26 


25.68 


4.07 


25.66 


4.18 


25.64 


4.29 


25.62 


4.40 


26 




27 


26.67 


4.22 


26.65 


4.34 


26.63 


4.46 


26.61 


4.57 


27 




28 


27.66 


4.38 


27.64 


4.50 


27.62 


4.62 


27.60 


4.74 


28 




29 


28.64 


4.54 


28.62 


4.66 


28.60 


4.79 


28.58 


4.91 


29 




30 


29.63 


4.69 


29.61 


4.82 


29.59 
30.57 


4.95 


29.57 


5.08 


30 




31 


30.62 


4.85 


30.60 


4.98 


5.12 


30.55 


5.25 


31 




32 


31.61 


5.01 


31.58 


5.14 


31.56 


5.28 


31.54 


5.42 


32 




33 


32.59 


5.16 


32.57 


5.30 


32.55 


5.45 


32.52 


5.59 


33 




34 


33.58 


5.32 


33.56 


5.47 


33.53 


5.61 


33.51 


5.76 


34 




35 


34.57 


5.48 


34.54 


5.63 


34.52 


5.78 


34.49 


5.93 


35 




36 


35.56 


5.63 


35.53 


5.79 


35.51 


5.94 


35.48 


6.10 


36 




37 


36.54 


5.79 


36.52 


5.95 


36.49 


6.11 


36.47 


6.27 


37 




38 


37.53 


5.94 


37.51 


6.11 


37.48 


6.27 


37.45 


6.44 


38 




39 


38.52 


6.10 


38.49 


6.27 


38.47 


6.44 


38.44 


6.60 


39 




40 


39.51 


6.26 


39.48 


6.43 


39.45 


6.60 


39.42 


6.77 


40 




41 


40.50 


6.41 


40.47 


6.59 


40.44 


6.77 


40.41 


6.94 


41 




42 


41.48 


6.57 


41.45 


6.75 


41.42 


6.92 


41.39 


7.11 


42 




43 


42.47 


6.73 


42.44 


6.91 


42.41 


7.10 


42.38 


7.28 


43 




44 


43.46 


6.88 


43.43 


7.07 


43.40 


7.26 


43.36 


7.45 


44 




45 


44.45 


7.04 


44.41 


7.23 


44.38 


7.43 


44.35 


7.62 


45 




46 


45.43 


7.20 


45.40 


7.39 


45.37 


7.59 


45.34 


7.79 


46 




47 


46.42 


7.35 


46.39 


7.55 


46.36 


7.76 


46.32 


7.96 


47 




48 


47.41 


7.51 


47.38 


7.72 


47.34 


7.92 


47.31 


8.13 


48 




49 


48.40 


7.67 


48.36 


7.88 


48.33 


8.09 


48.29 


8.30 


49 




50 

* 

a 

b 


49.38 


7.82 


49.35 


8.04 


49.32 


8.25 


49.28 


8.47 


50 




Dep. 
81 1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


CJ ■ 

1 

Q 




80$ 


Deg. 


80i 


Deg. 


80* 


De ? . 



TRAVERSE TABLE. 



21 



o 

o 


9 Deg. 


9i Deg. 


H Deg. 


9| Deg. 


o 




Lat. 


Dap. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 




51 


50.37 


7.98 


50.34 


8.20 


50.30 


8.42 


50.26 


8.64 


51 




5.2 


51.36 


8.13 


51.32 


8.36 


51.29 


8.58 


51.26 


8.81 


52 




53 


52.35 


8.29 


52.31 


8.52 


52.27 


8.75 


52.23 


8.9& 


53 




54 


53.34 


8.45 


53.30 


8.68 


53.26 


8.91 


53.22 


9.14 


54 




55 


54.32 


8.60 


54.28 


8.84 


54.25 


9.08 


54.21 


9.31 


55 




56 


55.31 


8.76 


55.27 


9.00 


55.23 


9.24 


55.19 


9.48 


56 




57 


56.30 


8.92 


56.26 


9.16 


56.22 


9.41 


56.18 


9.65 


57 




58 


57.29 


9.07 


57.25 


9.32 


57.20 


9.57 


57.16 


9.82 


58 




59 


58.27 


9.23 


58.23 


9.48 


58.19 


9.74 


58-15 


9.99 


59 




60 


59.26 


9.39 


59.22 


9.64 


59.18 


9.90 


59.13 


10.16 


60 


j 


61 


60.25 


9.54 


60.21 


9.81 


60.16 


10.07 


60.12 


10.33 


61 




62 


61.24 


9.70 


61.19 


9.97 


61.15 


10.23 


61.10 


10.50 


62 




63 


62.22 


9.86 


62.18 


10.13 


62.14 


10.40 


62.09 


10.67 


63 




64 


63.21 


10.01 


63.17 


10.29 


63.12 


10.56 


63.08 


10.84 


64 




65 


64.20 


10.17 


64.15 


10.45 


64.11 


10.73 


64.06 


11.01 


65 




66 


65.19 


10.32 


65.14 


10.61 


65.09 


10.89 


65.05 


11.18 


66 




67 


66.18 


10.48 


66.13 


10.77 


66.08 


11.06 


66.03 


11.35 


67 




68 


67.16 


10.64 


67.12 


10.93 


67.07 


11.22 


67.02 


11.52 


68 




69 


68.15 


10.79 


68.10 


11.09 


68.05 


11.39 


68.00 


11.69 


69 




70 


69.14 


10.95 


69.09 


11.25 


69.04 


11.55 


68.99 


11.85 


70 




71 


70.13 


11.11 


70.08 


11.41 


70.03 


11.72 


69.97 


12.02 


71 




72 


71.11 


11.26 


71.06 


11.57 


71.01 


11.88 


70.96 


12.19 


72 




73 


72.10 


11.42 


72.05 


11.73 


72.00 


12.05 


71.95 


12.36 


73 




74 


73.09 


11.58 


73.04 


11.89 


72.99 


12.21 


72.93 


12.53 


74 




75 


74.08 


11.73 


74.02 


12.06 


73.97 


12.38 


73.92 


12.70 


75 




76 


75.06 


11.89 


75.01 


12.22 


74.96 


12.54 


74.90 


12.87 


76 




77 


76.05 


12.05 


76.00 


12.38 


75.94 


12.71 


75.89 


13.04 


77 




78 


77.04 


12.20 


76.99 


12.54 


76.93 


12.87 


76.87 


13.21 


78 




79 


78.03 


12.36 


77.97 


12.70 


77.92 


13.04 


77.86 


13.38 


79 




80 


79.02 


12.51 


78.96 


12.86 


78.90 


13.20 


78.84 


13.55 


80 




81 


80.00 


12.67 


79.95 


13.02 


79.89 


13.37 


79.83 


13.72 


81 




82 


80.99 


12.83 


80.93 


13.18 


80.88 


13.53 


80.82 


13.89 


82 




83 


81.98 


12.98 


81.92 


13.34 


81.86 


13.70 


81.80 


14.06 


83 




84 


82.97 


13.14 


82.91 


13.50 


82.85 


13.86 


82.79 


14.23 


84 




85 


83.95 


13.30 


83.89 


13.66 


83.83 


14.03 


83.77 


14.39 


85 




86 


84.94 


13.45 


84.88 


13.82 


84.82 


14.19 


84.76 


14.56 


86 




87 


85.93 


13.61 


85.87 


13.98 


85.81 


14.36 


85.74 


14.73 


87 




88 


86.92 


13.77 


86.86 


14.15 


86.79 


14.52 


86.73 


14.90 


88 




89 


87.90 


13.92 


87.84 


14.31 


87.78 


14.69 


87.71 


15.07 


89 




90 


88.89 


14.08 


88.83 


14.47 


88.77 


14.85 


88.70 


15.24 


90 




91 


89.88 


14.24 


89.82 14.63 


89.75 


15.02 


89.69 


15.41 


91 




92 


90.87 


14.39 


90.80 


14.79 


90.74 


15.18 


90.67 


15.58 


92 




93 


91.86 


14.55 


91.79 


14.95 


91.72 


15.35 


91.66 


15.75 


93 




94 


92.84 


14.70 


92.78 


15.11 


92.71 


15.51 


92.64 


15.92 


94 




95 


93.83 


14.86 


93.76 


15.27 


93.70 


15.68 


93.63 


16.09 


95 




96 


94.82 


15.02 


94.75 


15.43 


94.68 


15.84 


94.61 


16.26 


96 




97 


95.81 


15.17 


95,74 


15.59 


95.67 


16.01 


95.60 


16.43 


97 




98 


96.79 


15.33 


96.73 


15.75 


96.66 


16.17 


96.58 


16.60 


98 




99 


97.78 


15.49 


97.71 


15.91 


97.64 


16.34 


97.57 


16.77 


99 




100 


98.77 


15.64 


98.70 


16.07 


98.63 


16.50 


98.56 


16.93 


100 




6 

3 

i 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


c 
S 




SI I 


)eg. 


801 Deg. 


Ml Deg. 


80i Deg. 





26 



22 



TRAVERSE TABLE. 



d 

ST 

3 
? 


10 Deg. 


10* Deg. 


10i Deg. 


10| Deg. 


C 

& 

a 

o 
a 


Lat. | 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.98 


0.17 


0.98 


0.18 


0.98 


0.18 i 


0.98 


0.19 


1 


2 


1.97 


0.35 


1.97 


0.36 


1.97 


0.36 1 


1.96 


0.37 


2 


3 


2.95 


0.52 


2.95 


0.53 


2.95 


0.55 | 


2.95 


0.56 


3 


4 


3.94 


0.69 


3.94 


0.71 


3.93 


0.73 


3.93 


0.75 


4 


5 


4.92 


0.87 


4.92 


0.89 


4.92 


0.91 


4.91 


0.93 


5 


6 


5.91 


1.04 


5.90 


1.07 


5.90 


1.09 


5.89 


1.12 


6 


7 


6.89 


1.22 


6.89 


1.25 


6.88 


1.28 


6.88 


1.31 


7 


8 


7.88 


1.39 


7.87 


1.42 


7.87 


1.46 


7.86 


1.49 


8 


9 


8.86 


1.56 


8.86 


1.60 


P. 85 


1.64 


8.84 


1.68 


9 


10 


9.85 


1.74 


9.84 


1.78 


9.83 


1.82 


9.82 


1.87 


10 


11 


10.83 


1.91 


10.82 


1.96 


10.82 


2.00 


10.81 


2.05 


11 


12 


11.82 


2.08 


11.81 


2.14 


11.80 


2.19 


11.79 


2.24 


12 


13 


12.80 


2.26 


12.79 


2.31 


12.78 


2.37 


12.77 


2.42 


13 


14 


13.79 


2.43 


13.78 


2.49 


13.77 


2.55 


13.75 


2.61 


14 


15 


14.77 


2.60 


14.76 


2.67 


14.75 


2.73 


14.74 


2.80 


15 


16 


15.76 


2.78 


15.74 


2.85 


15.73 


2.92 


15.72 


2.98 


16 


17 


16.74 


2.95 


16.73 


3.03 


16.72 


3.10 


16.70 


3.17 


17 


18 


17.73 


3.13 


17.71 


3.20 


17.70 


3.28 


17.68 


3.36 


18 


19 


18.71 


3.30 


18.70 


3.38 


18.68 


3.46 


18.67 


3.54 


19 


20 


19.70 


3.47 


19.68 


3.56 


19.67 


3.64 


19.65 


3.73 


20 


21 


20.68 


3.65 


20.66 


3.74 


20.65 


3.83 


20.63 


3.92 


21 


22 


21.67 


3.82 


21.65 


3.91 


21.63 


4.01 


21.61 


4.10 


22 


23 


22.65 


3.99 


22.63 


4.09 


22.61 


4.19 


22.60 


4.29 


23 


24 


23.64 


4.17 


23.62 


4.27 


23.60 


4.37 


23.58 


4.48 


24 


25 


24.62 


4.34 


24.60 


4.45 


24.58 


4.56 


24.56 


4.66 


25 


26 


25.61 


4.51 


25.59 


4.63 


25.56 


4.74 


25.54 


4.85 


26 


27 


26.59 


4.69 


26.57 


4.80 


26.55 


4.92 


26.53 


5.04 


27 


28 


27.57 


4.86 


27.55 


4.98 


27.53 


5.10 


27.51 


5.22 


28 


29 


28.56 


5.04 


28.54 


5.16 


28.51 


5.28 


28.49 


5.41 


29 


30 


29.54 


5.21 


29.52 


5.34 


29.50 


5.47 


29.47 


5.60 


30 


31 


30.53 


5.38 


30.51 


5.52 


30.48 


5.65 


30.46 


5.78 


31 


32 


31.51 


5.56 


31.49 


5.69 


31.46 


5.83 


31.44 


5.97 


32 


33 


32.50 


5.73 


32.47 


5.87 


32.45 


6.01 


32.42 


6.16 


33 


34 


33.48 


5.90 


33.46 


6.05 


33.43 


6.20 


33.40 


6.34 


34 


35 


34.47 


6.08 


34.44 


6.23 


34.41 


6.38 


34.39 


6.53 


35 


36 


35.45 


6.25 


35.43 


6.41 


35.40 


6.56 


35.37 


6.71 


36 


37 


36.44 


6.42 


36.41 


6.58 


36.38 


6.74 


36.35 


6.90 


37 


38 


37.42 


6.60 


37.39 


6.76 


37.36 


6.92 


37.33 


7.09 


38 


39 


38.41 


6.77 


38.38 


6.94 


38.35 


7.11 


38.32 


7.27 


39 


40 


39.39 


6.95 


39.36 


7.12 


39.33 


7.29 


39.30 


7.46 


40 


41 


40.38 


7.12 


40.35 


7.30 


40.31 


7.47 


40.28 


7.65 


41 


42 


41.36 


7.29 


41.33 


7.47 


41.30 


7.65 


41.26 


7.83 


42 


43 


42.35 


7.47 


42.31 


7.65 


42.28 


7.84 


42.25 


8.02 


43 


44 


43.33 


7.64 


43.30 


7.83 


43.26 


8.02 


43.23 


8.21 


44 


45 


44.32 


7.81 


44.28 


8.01 


44.25 


8.20 


44.21 


8.39 


45 


46 


45.30 


7.99 


45.27 


8.19 


45.23 


8.38 


45.19 


8.58 


46 


47 


46.29 


8.16 


46.25 


8.36 


46.21 


8.57 


46.18 


8.77 


47 


48 


47.27 


8.34 


47.23 


8.54 


47.20 


8.75 


47.16 


8.95 


48 


49 


48.26 


8.51 


48.22 


8.72 


48.18 


8.93 


48.14 


9 14 


49 


50 


49.24 


8.68 


49.20 


8.90 


49.16 


9.11 


, 49.12 


9.33 


50 


6 
o 

a 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

79* 


Lat. 
Deg. 


Dep. 


Lat. 


a 

c 

Q 


80 1 


Deg. 


79| 


Deg. 


79| Deg. 



TRAVERSE TABLE. 



23 



d 

3 

O 

' ? 


10 De-. 


104 Deg. 


10£ Deg. 


10| Deg. 


o 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




51 


50.23 


8.86 


50.19 


9.08 


50.15 


9.29 


50.10 


9.51 


51 




52 51.21 


9.03 


51.17 


9.25 


51.13 


9.48 


51.09 


9.70 


52 




53 


52.19 


9.20 


52.15 


9.43 


52.11 


9.66 


52.07 


9.89 


53 




54 


53.18 


9.38 


53.14 


9.61 


53.10 


9.84 


53.05 


10.07 


54 




55 


54.16 


9.55 


54.12 


9.79 


54.08 


10.02 


54.03 


10.26 


55 




56 


55.15 


9.72 


55.11 


9.96 


55.06 


10.21 


55.02 


10.45 


56 




57 


56.13 


9.90 


56.09 


10.14 


56.05 


10.39 


56.00 


10.63 


57 




58 


57.12 


10.07 


57.07 


10.32 


57.03 


10.57 


56.98 


10.82 


58 




59 


58.10 


10.25 


58.06 


10.50 


58.01 


10.75 


57.96 


11.00 


59 




60 


59.09 


10.42 


59.04 


10.68 


59.00 


10.93 


58.95 


11.19 


60 




61 


60.07 


10.59 


60.03 


10.85 


59.98 


11.12 


59.93 


11.38 


61 




62 


61.06 


10.77 


61.01 


11.03 


60.96 


11.30 


60.91 


11.56 


62 




63 


62.04 


10.94 


61.99 


11.21 


61.95 


11.48 


61.89 


11.75 


63 




64 


63.03 


11.11 


62.98 


11.39 


62.93 


11.66 


62.88 


11.94 


64 




65 


64.01 


11.29 


63.96 


11.57 


63.91 


11.85 


63.86 


12.12 


65 




66 


65.00 


11.46 


64.95 


11.74 


64.89 


12.03 


64.84 


12.31 


66 




67 


65.98 


11.63 


65.93 


11.92 


! 65.88 


12.21 


65.82 


12.50 


67 




I 68 


66.97 


11.81 


66.91 


12.10 


66.86 


12.39 


66.81 


12.68 


68 




1 69 


67.95 


11.98 


67.90 


12.28 


67.84 


12.57 


67.79 


12.87 


69 




70 


68.94 


12.16 


68.88 


12.46 


68.83 


12.76 


68.77 


13.06 


70 




71 


69.92 


12.33 


69.87 


12.63 


69.81 


12.94 


69.75 


13.24 


71 




72 


70.91 


12.50 


70.85 


12.81 


70.79 


13.12 


70.74 


13.43 


72 




73 


71.89 


12.68 


71.83 


12.99 


71.78 


13.30 


71.72 


13.62 


73 




74 


72.88 


12.85 


72.82 


13.17 


72.76 


13.49 


72.70 


13.80 


74 




75 


73.86 


13.02 


73.80 


13.35 


73.74 


13.67 


73.68 


13.99 


75 




76 


74.85 


13.20 


74.79 


13.52 


74.73 


13.85 


74.67 


14.18 


76 




77 


75.83 


13.37 


75.77 


13.70 


75.71 


14.03 


75.65 


14.36 


77 




78 


76.82 


13.54 


76.76 


13.88 


76.69 


14.21 


76.63 


J4.55 


78 




79 


77.80 


13.72 


77.74 


14.06 


77.68 


14.40 


77.61 


14.74 


79 




80 


78.78 


13.89 


78.72 


14.24 


78.66 


14.58 


78.60 


14.92 


80 




81 


79.77 


14.07 


79.71 


14.41 


79.64 


14.76 


79.58 


15.11 


81 




82 


80.75 


14.24 


80.69 


14.59 


80.63 


14.94 


80.56 


15.29 


82 




83 


81.74 


14.41 


81.68 


14.77 


81.61 


15.13 


81.54 


15.48 


83 




84 


82.72 


14.59 


82.66 


14.95 


82.59 


15.31 


82.53 


15.67 


84 




85 


83.71 


14.76 


83.64 


15.13 


83.58 


15.49 


83.51 


15.85 


85 




86 


84.69 


14.93 


84.63 


15.30 


84.56 


15.67 


84.49 


16.04 


86 




87 


85.68 


15.11 


85.61 


15.48 


85.54 


15.85 


85.47 


16.23 


87 




88 


86.66 


15.28 


86.60 


15.66 


86.53 


16.04 


86.46 


16.41 


88 




89 


87.65 


15.45 


87.58 


15.84 


87.51 


16.22 


87.44 


16.60 


89 




90 


88.63 


15.63 


88.56 


16.01 


88.49 


16.40 


88.42 


16.79 


90 




91 


89.62 


15.80 


89.55 


16.19 


89.48 


16.58 


89.40 


16.97 


91 




92 


90.60 


15.98 


90.53 


16.37 


90.46 


16.77 


90.39 


17.16 


92 




93 


91.59 


16.15 


91.52 


16.55 


91.44 


16.95 


91.37 


17.35 


93 




94 


92.57 


16.32 


92.50 


16.73 


92.43 


17.13 


92.35 


17.53 


94 




95 


93.56 


16.50 


93.48 


16.90 


93.41 


17.31 


93.33 


17.72 


95 




96 


94.54 


16.67 


94.47 


17.08 


94.39 


17.49 


94.32 


17.91 


96 




97 


95.53 


16.84 


95.45 


17.26 


95.38 


17.68 


95.30 


18.09 


97 




98 


96.51 


17.02 


96.44 


17.44 


96.36 


17.86 


96.28 


18.28 


98 




99 


97.50 


17.19 


97.42 


17.62 


97.34 


18.04 


97.26 


18.47 


99 




100 


98.48 


17.36 


98.40 


17.79 


98.33 


18.22 


98.25 


18.65 


100 




tt 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 


Dep. 


Lat. 


a 
5 




80 Deg. 


79| Deg. 


79i Deg. 


794 Deg. 





24 



TRAVERSE TABLE. 



o 

3 

a 
? 


11 Deg. 


Hi Deg. 


11* Deg. 


11 J Deg. 


O 

a 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.98 


0.19 


0.98 


0.20 


0.98 


0.20 


0.98 


0.20 


1 ■ 


2 


1.96 


0.38 


1.96 


0.39 


1.96 


0.40 


1.96 


0.41 


2 


3 


2.94 


0.57 


2.94 


0.59 


2.94 


0.60 


2.94 


0.61 


3 


4 


3.93 


0.76 


3.92 


0.78 


3.92 


0.80 


3.92 


0.82 


4 


5 


4.91 


0.95 


4.90 


0.98 


4.90 


1.00 


4.90 


1.02 


5 


6 


5.89 


1.14 


5.88 


1.17 


5.88 


1.20 


5.87 


1.22 


6 


7 


6.87 


1.34 


6.87 


1.37 


6.86 


1.40 


6.85 


1.43 


7 


8 


7.85 


1.53 


7.85 


1.56 


7.84 


1.59 


7.83 


1.63 


8 


9 


8.83 


1.72 


8.83 


1.76 


8.82 


1.79 


8.81 


1.83 


9 


10 


9.82 


1.91 


9.81 


1.95 


9.80 


1.99 


9.79 


2.04 


10 


11 


10.80 


2.10 


10.79 


2.15 


10.78 


2.19 


10.77 


2.24 


11 


12 


11.78 


2.29 


11.77 


2.34 


11.76 


2.39 


11.75 


2.44 


12 


13 


12.76 


2.48 


12.75 


2.54 


12.74 


2.59 


12.73 


2.65 


13 


14 


13.74 


2.67 


13.73 


2.73 


13.72 


2.79 


13.71 


2.85 


14 


IS 


14.72 


2.86 


14.71 


2.93 


14.70 


2.99 


14.69 


3.06 


15 


16 


15.71 


3.05 


15.69 


3.12 


15.68 


3.19 


15.66 


3.26 


16 


17 


16.69 


3.24 


16.67 


3.32 


16.66 


3.39 


16.64 


3.46 


17 


18 


17.67 


3.43 


17.65 


3.51 


17.64 


3.59 


17.62 


3.66 


18 


19 


18.65 


3.63 


18.63 


3.71 


18.62 


3.79 


18.60 


3.87 


19 


20 


19.63 


3.82 


19.62 


3.90 


19.60 


3.99 


19.58 


4 07 


20 


21 


20.61 


4.01 


20.60 


4.10 


20.58 


4.19 


20.56 


4.28 


21 


22 


21.60 


4.20 


21.58 


4.29 


21.56 


4.39 


21.54 


4.48 


22 


23 


22.58 


4.39 


22.56 


4.49 


22.54 


4.59 


22.52 


4.68 


23 


24 


23.56 


4.58 


23.54 


4.68 


23.52 


4.78 


23.50 


4.89 


24 


25 


24.54 


4.77 


24.52 


4.88 


24.50 


4.98 


24.48 


5.09 


25 


26 


25.52 


4.96 


25.50 


5.07 


25.48 


5.18 


25.46 


5.30 


26 


27 


26.50 


5.15 


26.48 


5.27 


26.46 


5.38 


26.43 


5.50 


27 


28 


27.49 


5.34 


27.46 


5.46 


27.44 


5.58 


27.41 


5.70 


28 


29 


28.47 


5.53 


28.44 


5.66 


28.42 


5.78 


28.39 


5.91 


29 


30 


29.45 


5.72 


29.42 


5.85 


29.40 


5.98 


29.37 


6.11 


30 


31 


30.43 


5.92 


30.40 


6.05 


30.38 


6.18 


30.35 


6.31 


31 


32 


31.41 


6.11 


31.39 


6.24 


31.36 


6.38 


31.33 


6.52 


32 ; 


33 


32.39 


6.30 


32.37 


6.44 


32.34 


6.58 


32.31 


6.72 


33 


34 


33.38 


6.49 


33.35 


6.63 


33.32 


6.78 


33.29 


6.92 


34 


35 


34.36 


6.68 


34.33 


6.83 


34.30 


6.98 


34.27 


7.13 


35 


36 


35.34 


6.87 


35.31 


7.02 


35.28 


7.18 


35.25 


7.33 


36 


37 


36.32 


7.06 


36.29 


7.22 


36.26 


7.38 


36.22 


7.53 


37 


38 


37.30 


7.25 


37.27 


7.41 


37.24 


7.58 


37.20 


7.74 


38 


39 


38.28 


7.44 


38.25 


7.61 


38.22 


7.78 


38.18 


7.94 


39 


40 


39.27 


7.63 


39.23 


7.80 


39.20 


7.97 


39.16 


8.15 


40 


41 


40.25 


7.82 


40.21 


8.00 


40.18 


8.17 


40.14 


8.35 


41 


42 


41.23 


8.01 


41.19 


8.19 


41.16 


8.37 


41.12 


8.55 


42 


43 


42.21 


8.20 


42.17 


8.39 


42.14 


8.57 


42.10 


8.76 


43 


44 


43.19 


8.40 


43.15 


8.58 


43.12 


8.77 


43.08 


8.96 


44 


45 


44.17 


8.59 


44.14 


8.78 


44.10 


8.97 


44.06 


9.16 


45 


46 


45.15 


8.78 


45.12 


8.97 


45.08 


9.17 


45.04 


9.37 


46 


47 


46.14 


8.97 


46.10 


9.17 


46.06 


9.37 


46.02 


9.57 


47 


1 48 


47.12 


9.16 


47.08 


9.36 


47.04 


9.57 


46.99 


9.78 


48 


I 49 


48.10 


9.35 


48.06 


9.56 


48.02 


9.77 


47.97 


9.98 


49 


| 50 


49.08 


9.54 


49.04 


9.75 


49.00 


9.97 


48.95 


10.18 


50 


<u 
o 
a 
rt 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i 


79 1 


)eg. 


,3, 


Deg. 


78J Deg. 


78i 


Deg. 



TRAVERSE TABLE. 



25 



g 

V 

3 

a 
a 


11 Deg. 


Hi Deg. 


Hi Deg. 


Ill Deg. 


C 

a 

o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Lep. 


51 


50.06 


9.73 


50.02 


9.95 


49.98 


10.17 


49.93 


10.39 


51 


52 


51.04 


9.92 


51.00 


10.14 


50.96 


10.37 


50.91 


10.59 


52 


53 


52.03 


10.11 


51.98 


10.34 


51.94 


10.57 


51.89 


10.79 


53 


54 


53.01 


10.30 


52.96 


10.53 


52.92 


10.77 


52.87 


11.00 


54 


55 


53.99 


10.49 


53.94 


10.73 


53.90 


10.97 


53.85 


11.20 


55 


56 


54.97 


10.69 


54.92 


10.93 


54.88 


11.16 


54.83 


11.40 


56 


51 


55.95 


10.88 


55.90 


11.12 


55.86 


11.36 


55.81 


11.61 


57 


58 


56.93 


11.07 


56.89 


11.32 


56.84 


11.56 


56.78 


11.81 


58 


59 


57.92 


11.26 


57.87 


11.51 


57.82 


11.76 


57.76 


12.01 


59 


60 


58.90 


11.45 


58.85 


11.71 


58.80 


11.96 


58.74 


12.22 


60 


1 61 


5£ 88 


11.64 


59.83 


11.90 


59.78 


12.16 


59.72 


12.42 


61 


62 


60.86 


11.83 


60.81 


12.10 


60.76 


12.36 


60.70 


12.63 


62 


63 


61.84 


12.02 


61.79 


12.29 


61.74 


12.56 


61.68 


12.83 


63 


64 


62.82 


12.21 


62.77 


12.49 


62.72 


12.76 


62.66 


3.03 


64 


65 


63.81 


12.40 


63.75 


12.68 


63.70 


12.96 


63.64 


13.24 


65 


66 


64.79 


12.59 


64.73 


12.88 


64.68 


13.16 


64.62 


13.44 


66 


67 


65.77 


12.78 


65.71 


13.07 


65.66 


13.36 


65.60 


13.64 


67 


68 


66.75 


12.98 


66.69 


13.27 


66.63 


13.56 


66.58 


13.85 


68 


69 


67.73 


13.17 


67.67 


13.46 


67.61 


13.76 


67.55 


14.05 


69 


70 


68.71 


13.36 


68.66 


13.66 


68.59 


13.96 


68.53 


14.25 


70 


71 


69.70 


13.55 


69.64 


13.85 


69.57 


14.16 


69.51 


14.46 


71 


72 


70.68 


13.74 


70.62 


14.05 


70.55 


14.35 


70.49 


14.66 


72 


73 


71.66 


13.93 


71.60 


14.24 


71.53 


14.55 


71.47 


14.87 


73 


74 


72.64 


14.12 


72.58 


14.44 


72.51 


14.75 


72.45 


15.07 


74 


75 


73.62 


14.31 


73.56 


14.63 


73.49 


14.95 


73.43 


15.27 


75 


76 


74.60 


14.50 


74.54 


14.83 


74.47 


15.15 


74.41 


15.48 


76 


77 


75.59 


14.69 


75.52 


15.02 


75.45 


15.35 


75.39 


15.68 


77 


78 


76.57 


14.88 


76.50 


15.22 


76.43 


15.55 


76.37 


15.88 


78 


79 


77.55 


15.07 


77.48 


15.41 


77.41 


15.75 


77.34 


16.09 


79 


80 


78.53 


15.26 


78.46 


15.61 


78.39 


15.95 


78.32 


16.29 


80 


81 


79.51 


15.46 


79.44 


15.80 


79.37 


16.15 


79.30 


16.49 


81 


82 


80.49 


15.65 


80.42 


16.00 


80.35 


16.35 


80.28 


16.70 


82 


83 


81.48 


15.84 


81.41 


16.19 


81.33 


16.55 


81.26 


16.90 


83 


84 


82.46 


16.03 


82.39 


16.39 


82.31 


16.75 


82.24 


17.11 


84 


85 


83.44 


16.22 


83.37 


16.58 


83.29 


16.95 


83.22 


17.31 


85 


86 


84.42 


16.41 


84.35 


16.78 


84.27 


17.15 


84.20 


17.51 


86 


87 


85.40 


16.60 


85.33 


16.97 


85.25 


17.35 


85.18 


17.72 


87 


88 


86.38 


16.79 


86.31 


17.17 


86.23 


17.54 


86.16 


17.92 


88 


89 


87.36 


16-98 


87.29 


17.36 


87.21 


17.74 


87.14 


18.12 


89 


90 


88.35 


17.. 7 


88.27 


17.56 


88.19 


17.94 


88.11 


18.33 


90 


91 


89.33 


17.36 


89.25 


17.75 


89.17 


18.14 


89.09 


18.53 


91 


92 


90.31 


17.55 


90.23 


17.95 


90.15 


18.34 


90.07 


18.74 


92 


93 


91.29 17.75 


91.21 


18.14 


91.13 


18.54 


91.05 


18.94 


93 


94 


92.27 


17.94 


92.19 


18.34 


92.11 


18.74 


92.03 


19.14 


94 


95 


93.25 


18.13 


93.17 


18.53 


93.09 


18.94 


93.01 


19.35 


95 


96 


94.24 


18.32 


94.16 


18.73 


94.07 


19.14 


93.99 


19.55 


96 


97 


95.22 


18.51 


95.14 


18.92 


95.05 


19.34 


94.97 


19.75 


97 


98 


96.20 


18.70 


96.12 


19.12 


96.03 


19.54 


95.95 


19.96 


98 


99 


97.18 


18.89 


97.10 


19.31 


97.01 


19.74 


96.93 


20.16 


99 


100 


98.16 


19.08 


98.08 


19.51 


97.99 


19.94 


97.90 


20.36 


100 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. | Lat. 


o 


79 Deg. 


78| Deg. 

I 


78£ Deg. 


78i Deg. 



26* 



2Q 



26 



TRAVERSE TABLE 



3" 

o 
? 


12 Deg. 


124 Deg. 


12i Deg. 


12* Deg. 


g 

o 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.98 


0.21 


0.98 


0.21 


0.98 


0.22 


0.98 


0.22 


1 


2 


1.96 


0.42 


1.95 


0.42 


1.95 


0.43 


1.95 


0.44 


2 


3 


2.93 


0.62 


2.93 


0.64 


2.93 


0.65 


2.93 


0.66 


3 


4 


3.91 


0.83 


3.91 


0.85 


3.91 


0.87 


3.90 


0.88 


4 


5 


4.89 


1.04 


4.89 


1.06 


4.88 


1.08 


4.88 


1.10 


5 


6 


5.87 


1.25 


5.86 


1.27 


5.86 


1.30 


5.85 


1.32 


6 


7 


6.85 


1.46 


6.84 


1.49 


6.83 


1.52 


6.83 


1.54 


7 


8 


7.83 


1.66 


7.82 


1.70 


7.81 


1.73 


7.80 


1.77 


8 


9 


8.80 


1.87 


8.80 


1.91 


8.79 


1.95 


8.78 


1.99 


9 


10 


9.78 


2.08 


9.77 


2.12 


9.76 


2.16 


9.75 


2.21 


10 


11 


10.76 


2.29 


10.75 


2.33 


10.74 


2.38 


10.73 


2.43 


11 


12 


11.74 


2.49 


11.73 


2.55 


11.72 


2.60 


11.70 


2.65 


12 


13 


12.72 


2.70 


12.70 


2.76 


12.69 


2.81 


12.68 


2.87 


13 


14 


13.69 


2.91 


13.68 


2.97 


13.67 


3.03 


13.65 


3.09 


14 


15 


14.67 


3.12 


14.66 


3.18 


14.64 


3.25 


14.63 


3.31 


15 


16 


15.65 


3.33 


15.64 


3.39 


15.62 


3.46 


15.61 


3.53 


16 


17 


16.63 


3.53 


16.61 


3.61 


16.60 


3.68 


16.58 


3.75 


17 


18 


17.61 


3.74 


17.59 


3.82 


17.57 


3.90 


17.56 


3.97 


18 


19 


18.58 


3.95 


18.57 


4.03 


18.55 


4.11 


18.53 


4.19 


19 


20 


19.56 


4.16 


19.54 


4.24 


19.53 


4.33 


19.51 


4.41 


20 


21 


20.54 


4.37 


20.52 


4.46 


20.50 


4.55 


20.48 


4.63 


21 


22 


21.52 


4.57 


21.50 


4.67 


21.48 


4.76 


21.46 


4.86 


22 


23 


22.50 


4.78 


22.48 


4.88 


22.45 


4.98 


22.43 


5.08 


23 


24 


23.48 


4.99 


23.45 


5.09 


23.43 


5.19 


23.41 


5.30 


24 


25 


24.45 


5.20 


24.43 


5.30 


24.41 


5.41 


24.38 


5.52 


25 


26 


25.43 


5.41 


25.41 


5.52 


25.38 


5.63 


25.36 


5.74 


26 


27 


26.41 


5.61 


26.39 


5.73 


26.36 


5.84 


26.33 


5.96 


27 


28 


27.39 


5.82 


27.36 


5-94 


27.34 


6.06 


27.31 


6.18 


28 


29 


28.37 


6.03 


28.34 


6.15 


28.31 


6.28 


28.28 


6.40 


29 


30 


29.34 


6.24 


29.32 


6.37 


29.29 


6.49 


29.26 


6.62 


30 


31 


30.32 


6.45 


30.29 


6.58 


30.27 


6.71 


30.24 


6.84 


31 


32 


31.30 


6.65 


31.27 


6.79 


31.24 


6.93 


31.21 


7.06 


32 


33 


32.28 


6.86 


32.25 


7.00 


32.22 


7.14 


32.19 


7.28 


33 


34 


33.26 


7.07 


33.23 


7.21 


33.19 


7.36 


33.16 


7.50 


34 


:15 


34.24 


7.28 


34.20 


7.43 


34.17 


7.53 


34.14 


7.72 


35 


36 


35.21 


7.48 


35.18 


7.64 


35.15 


7.79 


35.11 


7.95 


36 


37 


36.19 


7.69 


36.13 


7.85 


36.12 


8.01 


36.09 


8.17 


37 


38 


37.17 


7.90 


37.13 


8.06 


37.10 


8.22 


37.06 


8.39 


38 


39 


38.15 


8.11 


38.11 


8.27 


38.03 


8.44 


38.04 


8.61 


39 


40 


39.13 


8.32 


39.09 


8.49 


39.05 


8.66 


39.01 


8.83 


40 


41 


40.10 


8.52 


40.07 


8.70 


40.03 


8.87 


39.99 


9.05 


41 


42 


41.08 


8.73 


41.04 


8.91 


41.00 


9.09 


40.96 


9.27 


42 


43 


42.06 


8.94 


42.02 


9.12 


41.98 


9.31 


41.94 


9.49 


43 


44 


43.04 


9.15 


43.00 


9.34 


42.96 


9.52 


42.92 


9.71 


44 


45 


44.02 


9.36 


43.98 


9.55 


43.93 


9.74 


43.89 


9.93 


45 


46 


44.99 


9.56 


44.95 


9.76 


44.91 


9.96 


44.87 


10.15 


46 


47 


45.97 


9.77 


45.93 


9.97 


45.89 


10.17 


45.84 


10.37 


47 


48 


46.95 


9.98 


46.91 


10.18 


46.86 


10.39 


46.82 


10.59 


48 


49 


47.93 


10.19 


47.88 


10.40 


47.84 


10.61 


47.79 


10.81 


49 


50 


48.91 


10.40 


48.86 


10.61 


48.81 


10.82 


48.77 


11.03 


50 


6 

a 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


09 

O 

c 
.2 

s 


78 ] 


Deg. 


77| 


Deg. 


77£ 


Deg. 


77J Deg. 



TRAVERSE TABLE. 



27 



g 

p 

o 


12 Deg. 


12\ Deg. 


m Deg. 


12| Deg. 


If 

o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


49.89 


10.60 


49.84 


10.82 


49.79 


11.04 


49.74 


11.26 


51 


52 


50.86 


10.81 


50.82 


11.03 


50.77 


11.25 


50.72 


11.48 


52 


53 


51.84 


11.02 


51.79 


11.25 


51.74 


11.47 


51.69 


11.70 


53 ' 


54 


52.82 


11.23 


52.77 


11.46 


52.72 


11.69 


52.67 


11.92 


54 


55 


53.80 


11.44 


53.75 


11.67 


53.70 


11.90 


53.64 


12.14 


55 


56 


54.78 


11.64 


54.72 


11.88 


54.67 


12.12 


54.62 


12.36 


56 ' 


57 


55.75 


11.85 


55.70 


12.09 


55.65 


12.34 


55.59 


12.58 


57 . 


58 


56.73 


12.06 


56.68 


12.31 


56.63 


12.55 


56.57 


12.80 


58 


59 


57.71 


12.27 


57.66 


12.52 


57.60 


12.77 


57.55 


13.02 


59 


60 


58.69 


12.47 


58.63 


12.73 


58.58 


12.99 


58.52 


13.24 


60 . 


61 


59.67 


12.68 


59.61 


12-94 


59.55 


13.20 


59.50 


13.46 


61 


62 


60.65 


12.89 


60.59 


13.16 


60.53 


13.42 


60.47 


13.68 


62 


63 


61.62 


13.10 


61.57 


13.37 


61.51 


13.64 


61.45 


13.90 


63 


64 


62.60 


13.31 


62.54 


13.58 


62.48 


13.85 


62.42 


14.12 


64 


65 


63.58 


13.51 


63.52 


13.79 


63.46 


14.07 


63.40 


14.35 


65 ' 


66 


64.56 


13.72 


64.50 


14.00 


64.44 


14.29 


64.37 


14.57 


66 


67 
68 


65.54 


13.93 


65.47 


14.22 


65.41 


14.50 


65.35 


14.79 


67 


66.51 


14.14 


66.45 


14.43 


66.39 


14.72 


66.32 


15.01 


68 


69 


67.49 


14.35 


67.43 


14.64 


67.36 


14.93 


67.30 


15.23 


69 


70 


68.47 


14.55 


68.41 


14.85 


68.34 


15.15 


68.27 


15.45 


70 


71 


69.45 


14.76 


69.38 


15.06 


69.32 


15.37 


69.25 


15.67 


71 


72 


70.43 


14.97 


70.-36 


15.28 


70.29 


15.58 


70.22 


15.89 


72 


73 


71.40 


15.18 


71.34 


15.49 


71.27 


15.80 


71.20 


16.11 


<3 


74 


72.38 


15.39 


72.32 


15.70 


72.25 


16.02 


72.18 


16.33 


74 


75 


73.36 


15.59 


73.29 


15.91 


73.22 


16.23 


73.15 


16.55 


75 


76 


74.34 


15.80 


74.27 


16.13 


74.20 


16.45 


74.13 


16.77 


76 ' 


77 


75.32 


16.01 


75,25 


16.34 


75.17 


16.67 


75.10 


16.99 


77 


78 


76.30 


16.22 


76.22 


16.55 


76.15 


16.88 


76.08 


17.21 


78 


79 


77.27 


16.43 


77.20 


16.76 


77.13 


17.10 


77.05 


17.44 


79 


80 


78.25 


16.63 


78.18 


16.97 


78.10 


17.32 


78.03 


17.66 


80 


81 


79.23 


16.84 


79.16 


17.19 


79.08 


17.53 


79.00 


17.88 


81 ■ 


82 


80.21 


17.05 


80.13 


17.40 


80.06 


17.75 


79.98 


18.10 


82 


83 


81.19 


17.26 


81.11 


17.61 


81 .03 


17.96 


80.95 


18.32 


83 


84 


82.16 


17.46 


82.09 


17.82 


82.01 


18.18 


81.93 


18.54 


84 1 


85 


83.14 


17.67 


83.06 


18.04 


82.99 


18.40 


82.90 


18.76 


85 


86 


84.12 


17.88 


84.04 


18.25 


83.96 


18.61 


83.88 


18.98 


86 1 


87 


85.10 


18.09 


85.02 


18.46 


84.94 


18.83 


84.85 


19.20 


87 


88 


86.08 


18.30 


86.00 


18.67 


85.91 


19.05 


85.83 


19.42 


88 


89 


87.06 


18.50 


86.97 


18.88 


86.89 


19.26 


86.81 


19.64 


89 


90 


88.03 


18.71 


87.95 


19.10 


87.87 


19.48 


87.78 


19.86 


90 


91 


89.01 


18.92 


88.93 


19.31 


88.84 


19.70 


88.76 


20.08 


91 


92 


89.99 


19.13 


89.91 


19.52 


89.82 


19.91 


89.73 


20.30 


92 


93 


90.97 


19.34 


90.88 


19.73 


90.80 


20.13 


90.71 


20.52 


93 : 


94 


91.95 


19.54 


91.86 


19.94 


91.77 


20.35 


91.68 


20.75 


94 


95 


92.92 


19.75 


92.84 


20.16 


92.75 


20.56 


92.66 


20.97 


95 


96 


93.90 


19.96 


93.81 


20.37 


93.72 


20.78 


93.63 


21.19 


96 


97 


94.88 


20.17 


94.79 


20.58 


94.70 


20.99 


94.61 


21.41 


97 


98 


95.86 


20.38 


95.77 


20.79 


95.68 


21.21 


95.58 


21.63 


98 


99 


96.84 


20.58 


96.75 


21.01 


96.65 


21.43 


96.56 


21.85 


99 


100 


97.81 


20.79 


97.72 


21.22 


97.63 


21.64 


97.53 


22.07 


100 


o 
B 
a 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


d 

o 

c 

5 ; 


78 Deg. 


77| Deg. 


77i 


Deg. 


77i 


Deg. 



28 



TRAVERSE TABLE. 



a 

o 

? 


13 Deg. 


13{ Deg. 


134 Deg 


13| Deg. 


§ 

3 
O 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


j 


0.97 


0.23 


0.97 


0.23 


0.97 


0.23 


0.97 


0.24 


1 


2 


1.95 


0.45 


1.95 


0.46 


1.95 


0.47 


1.94 


0.48 


2 


3 


2.92 


0.67 


2.92 


0.69 


2.92 


0.70 


2.91 


0.71 


3 


4 


3.90 


0.90 


3.89 


0.92 


3.89 


0.93 


3.89 


0.95 


4 


5 


4.87 


1.12 


4.87 


1.15 


4.86 


1.17 


4.86 


1.19 


5 


6 


5.85 


1.35 


5.84 


1.38 


5.83 


1.40 


5.83 


1.43 


6 


7 


6.82 


1.57 


6.81 


1.60 


6.81 


1.63 


6.80 


1.66 


7 


8 


7.80 


1.80 


7.79 


1.83 


7.78 


1.87 


7.77 


1.90 


8 


9 


8.77 


2.02 


8.76 


2.06 


8.75 


2.10 


8.74 


2.14 


9 


10 


9.74 


2.25 


9.73 


2.29 


9.72 


2.33 


9.71 


2.38 


10 


11 


10.72 


2.47 


10.71 


2.52 


10.70 


2.57 


10.68 


2.61 


11 


12 


11.69 


2.70 


11.68 


2.75 


11.67 


2.80 


11.66 


2.85 


12 


13 


12.67 


2.92 


12.65 


2.98 


12.64 


3.03 


12.63 


3.09 


13 


14 


13.64 


3.15 


13.63 


3.21 


13.61 


3.27 


13.60 


3.33 


14 


15 


14.62 


3.37 


14.60 


3.44 


14.59 


3.50 


14.57 


3.57 


15 


16 


15.59 


3.60 


15.57 


3.67 


15.56 


3.74 


15.54 


3.80 


16 


17 


16.57 


3.82 


16.55 


3.90 


16.53 


3.97 


16.51 


4.04 


17 


18 


17.54 


4.05 


17.52 


4.13 


17.50 


4.20 


17.48 


4.28 


18 


19 


18.51 


4.27 


18.49 


4.35 


18.48 


4.44 


18.46 


4.52 


19 


20 


19.49 


4.50 


19.47 


4.58 


19.45 


4.67 


19.43 


4.75 


20 


21 


20.46 


4.72 


20.44 


4.81 


20.42 


4.90 


20.40 


4.99 


21 


22 


21.44 


4.95 


21.41 


5.04 


21.39 


5.14 


21.37 


5.23 


22 


23 


22.41 


5.17 


22.39 


5.27 


22.36 


5.37 


22.34 


5.47 


23 


24 


23.38 


5.40 


23.36 


5.50 


23.34 


5.60 


23.31 


5.70 


24 


25 


24.36 


5.62 


24.33 


5.73 


24.31 


5.84 


24.28 


5.94 


25 


26 


25.33 


5.85 


25.31 


5.96 


25.28 


6.07 


25.25 


6.18 


26 


27 


26.31 


6.07 


26.28 


6.19 


26.25 


6.30 


26.23 


6.42 


27 


28 


27.28 


6.30 


27.25 


6.42 


27.23 


6.54 


27.20 


6.66 


28 


29 


28.26 


6.52 


28.23 


6.65 


28.20 


6.77 


28.17 


6.89 


29 


30 


29.23 


6.75 


29.20 


6.88 


29.17 


7.00 


29.14 


7.13 


30 


31 


30.21 


6.97 


30.17 


7.11 


30.14 


7.24 


30.11 


7.37 


31 


32 


31.18 


7.20 


31.15 


7.33 


31.12 


7.47 


31.08 


7.61 


32 


33 


32.15 


7.42 


32.12 


7.56 


32.09 


7.70 


32.05 


7.84 


33 


34 


33.13 


7.65 


33.09 


7.79 


33.06 


7.94 


33.03 


8.08 


34 


35 


34.10 


7.87 


34.07 


8.02 


34.03 


8.17 


34.00 


8.32 


35 


36 


35.08 


8.10 


35.04 


8.25 


35.01 


8.40 


34.97 


8.56 


36 


37 


36.05 


8.32 


36.02 


8.48 


35.98 


8.64 


35.94 


8.79 


37 


38 


37.03 


8.55 


36.99 


8.71 


36.95 


8.87 


36.91 


9.03 


38 


39 


38.00 


8.77 


37.96 


8.94 


37.92 


9.10 


37.88 


9.27 


39 


40 


38.97 


9.00 


38.94 


9.17 


38.89 


9.34 


38.85 


9.51 


40 


41 


39.95 


9.22 


39.91 


9.40 


39.87 


9.57 


39.83 


9.75 


41 


42 


40.92 


9.45 


40.88 


9.63 


40.84 


9.80 


40.80 


9.98 


42 


43 


41.90 


9.67 


41.86 


9.86 


41.81 


10.04 


41.77 


10.22 


43 


44 


42.87 


9.90 


42.83 


10.08 


42.78 


10.27 


42.74 


10.46 


44 


45 


43.85 


10.12 


43.80 


10.31 


43.76 


10.51 


43.71 


10.70 


45 


46 


44.82 


10.35 


44.78 


10.54 


44.73 


10.74 


44.68 


10.93 


46 


47 


45.80 


10.57 


45.75 


10.77 


45.70 


10.97 


45.65 


11.17 


47 


48 


46.77 


10.80 


46.72 


11.00 


46.67 


11.21 


46.62 


11.41 


48 


49 


47.74 


11.02 


47.70 


11.23 


47.65 


11.44 


47.60 


11.65 


49 


50 


48.72 


11.25 


48.67 


11.46 


48.62 


11.67 


48.57 


11.88 


50 : 


a 
a 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


• 

o 

a 

a 

5 


77] 


*& 


76| 


Deg. 


76* Deg. 


764 


Deg. 



TRAVERSE TABLE. 



29 





3 

a 

a 


13 Deg. 


13* Deg. 


13* Deg. 


13| Deg. 


C 
ST 

CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


49.69 


11.47 


49.64 


11.69 


49.59 


11.91 


49.54 


12.12 


51 


52 


50.67 


11.70 


50.62 


11.92 


50.56 


12.14 


50.51 


12.36 


52 


53 


51.64 


11.92 


51.59 


12.15 


51.54 


12.37 


51.48 


12.60 


53 


54 


52.62 


12.15 


52.56 


12.38 


52.51 


12.61 


52-45 


12.84 


54 


55 


53.59 


12.37 


53.54 


12.61 


53.48 


12.84 


53.42 


13.07 


55 


56 


54.56 


12.60 


54.51 


12.84 


54-45 


13.07 


54.40 


13.31 


56 


57 


55.54 


12.82 


55.48 


13.06 


55.43 


13.31 


55.37 


13.55 


57 


53 


56.51 


13.05 


56.46 


13.29 


56.40 


13.54 


56.34 


13.79 


58 


59 


57.49 


13.27 


57.43 


13.52 


57.37 


13.77 


57.31 


14.02 


59 


60 


58.46 


13.50 


58.40 


13.75 


58.34 


14.01 


58.28 


14.26 


60 


61 


59.44 


13.72 


59.38 


13.98 


59.31 


14.24 


59.25 


14.50 


61 


62 


60.41 


13.95 


60.35 


14.21 


60.29 


14.47 


60.22 


14.74 


62 


63 


61.39 


14.17 


61.32 


14.44 


61.26 


14.71 


61.19 


14.97 


63 


64 


62.36 


14.40 


62.30 


14.67 


62.23 


14.94 


62.17 


15.21 


64 


65 


63.33 


14.62 


63.27 


14.90 


63.20 


15.17 


€3.14 


15.45 


65 [ 


66 


64.31 


14.85 


64.24 


15.13 


64.18 


15.41 


64.11 


15.69 


66 


67 


65.28 


15.07 


65.22 


15.36 


65.15 


15.64 


65.08 


15.93 


67 


68 


66.26 


15.30 


66.19 


15.59 


66.12 


15.87 


66.05 


16.16 


68 


69 


67.23 


15.52 


67.16 


15.81 


67.09 


16.11 


67.02 


16.40 


69 


70 


68.21 


15.75 


68.14 


16.04 


68.07 


16.34 


67.99 


16.64 


70 


71 


69.18 


15.97 


69.11 


16.27 


69.04 


16.57 


68.97 


16.88 


71 


72 


70.15 


16.20 


70.08 


16.50 


70.01 


16.81 


69.94 


17.11 


72 


73 


71.13 


16.42 


71.06 


16.73 


70.98 


17.04 


70.91 


17.35 


73 


74 


72.10 


16.65 


72.03 


16-96 


71.96 


17.28 


71.88 


17.59 


74 


75 


73.08 


16.87 


73.00 


17.19 


72.93 


17.50 


72.85 


17.83 


75 


76 


74.05 


17.10 


73.98 


17.42 


73.90 


17.74 


73.82 


18.06 


76 


77 


75.03 


17.32 


74.95 


17.65 


74.87 


17.98 


74.79 


18.30 


77 


78 


76.00 


17.55 


75.92 


17.88 


75.84 


18.21 


75.76 


18.54 


78 


79 


76.98 


17.77 


76.90 


18.11 


76.82 


18.44 


76.74 


18.78 


79 


80 


77.95 


18.00 


77.87 


18.34 


77.79 


18.68 


77.71 


19.01 


80 


81 


78.92 


18.22 


78.84 


18.57 


78.76 


18.91 


78.68 


19.25 


81 


82 


79.90 


18.45 


79.82 


18.79 


70.73 


19.14 


79.65 


19.49 


82 


83 


80.87 


18.67 


80.79 


19.02 


80.71 


19.38 


80.62 


19.73 


S3 


84 


81.85 


18.90 


81.76 


19.25 


81.68 


19.61 


81.59 


19.97 


84 


85 


82.82 


19.12 


82.74 


19.48 


82.65 


19.84 


82.56 


20.20 


85 


86 


83.80 


19.35 


83.71 


19.71 


83.62 


20.03 


83.54 


20.44 


86 


87 


84.77 


19.57 


84.68 


19.94 


84.60 


20.31 


84.51 


20.68 


87 


88 


85.74 


19.80 


85.66 


20.17 


85.57 


20.54 


85.48 


20.92 


88 


89 


86.72 


20.02 


86.63 


20.40 


86.54 


20.78 


86.45 


21.15 


89 


90 


87.69 


20.25 


87.60 


20.63 


87.51 


21.01 


87.42 


21.39 


90 


91 


88.67 


20.47 


88.58 


20.86 


88.49 


21.24 


88.39 


21.63 


91 


92 


89.64 


20.70 


89.55 


21.09 


89.46 


21.48 


89.36 


21.87 


92 


93 


90.62 


20.92 


90.52 


21.32 


90.43 


21.71 


90-33 


22.10 


93 


94 


91.59 


21.15 


91.50 


21.54 


91.40 


21.94 


91.31 


22.34 


94 


95 


92.57 


21.37 


92.47 


21.77 


92.38 


22.18 


92.28 


22.58 


95 


96 


93.54 


21.60 


93.44 


22.00 


93.35 


22.41 


93.25 


22.82 


96 


97 


94.51 


21.82 


94.42 


22.23 


94.32 


22.64 


94.22 


23.06 


97 


98 


95.49 


22.05 


95.39 


22.46 


95.29 


22.88 


95.19 


23.29 


98 


99 


96.46 


22.27 


96.36 


22.69 


96.26 


23.11 


96.16 


23.53 


99 


100 


97.44 


22.50 


97.34 


22.92 


97.24 


23.34 


97.13 


23.77 


100 


s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 

a 

S ' 


77 1 


>eg. 


761 


Deg. 


76£ Deg. 


76* 


Deg. 



30 



TRAVERSE TABLE. 



d 

O 


14 Deg. 


Ui 


Deg. 


14i Deg. 


14} 


Deg. 




o 

a 

1 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


0.97 


0.24 


0.97 


0.25 


0.97 


0.25 


0.97 


0.25 






1.94 


0.48 


1.94 


0.49 


1.94 


0.50 


1.93 


0.51 


2 




3 


2.91 


0.73 


2.91 


0.74 


2.90 


0.75 


2.90 


0.76 


3 




1 4 


3-88 


0.97 


3.88 


0.98 


3.87 


1.00 


3.87 


1.02 


4 




5 


4.85 


1.21 


4.85 


1.23 


4.84 


1.25 


4.84 


1.27 


5 




6 


5.82 


1.45 


5.82 


1.48 


5.81 


1.50 


5.80 


1.53 


6 




7 


6.79 


1.69 


6.78 


1.72 


6.78 


1.75 


6.77 


1.78 


7 




8 


7.76 


1.94 


7.75 


1.97 


7.75 


2.00 


7.74 


2.04 


8 




9 


8.73 


2.18 


8.72 


2.22 


8.71 


2.25 


8.70 


2.29 


9 




10 


9.70 


2.42 


9.69 


2.46 


9.68 


2.50 


9.67 


2.55 


10 




11 


10.67 


2.66 


10.66 


2.71 


10.65 


2.75 


10.64 


2.80 


11 




12 


11.64 


2.90 


11.63 


2.95 


11.62 


3.00 


11.60 


3.06 


12 




13 


12.61 


3.15 


12.60 


S.20 


12.59 


3.25 


12.57 


3.31 


13 




14 


13.58 


3.39 


13.57 


3.45 


13.55 


3.51 


13.54 


3.56 


14 




15 


14.55 


3.63 


14.54 


3.69 


14.52 


3.76 


14.51 


3.82 


15 




16 


15.52 


3.87 


15.51 


3.94 


15.49 


4.01 


15.47 


4.07 


16 




17 


16.50 


4.11 


16.48 


4.18 


16.46 


4.26 


16.44 


4.33 


17 




13 


17.47 


4.35 


17.45 


4.43 


17.43 


4.51 


17.41 


4.58 


18 




19 


18.44 


4.60 


18.42 


4.68 


18.39 


4.76 


18.37 


4.84 


19 




20 


19.41 


4.84 


19.38 


4.92 


19.36 


5.01 


19.34 


5.09 


20 




21 


20.38 


5.08 


20.35 


5.17 


20.33 


5.26 


20.31 


5.35 


21 




22 


21.35 


5.32 


21.32 


5.42 


21.30 


5.51 


21.28 


5.60 


22 




23 


22.32 


5.56 


22.29 


5.66 


22.27 


5.76 


22.24 


5.86 


23 




24 


23.29 


5.81 


23.26 


5.91 


23.24 


6.01 


23.21 


6.11 


24 




25 


24.26 


6.05 


24.23 


6.15 


24.20 


6.26 


24.18 


6.37 


25 




26 


25.23 


6.29 


25.20 


6.40 


25.17 


6.51 


25.14 


6.62 


26 




27" ■ 


26.20 


6.53 


26.17 


6.65 


26.14 


6.76 


26.11 


6.87 


27 




28 


27.17 


6.77 


27.14 


6.89 


27.11 


7.01 


27.08 


7.13 


28 




29 


28.14 


7.02 


28.11 


7.14 


28.08 


7.26 


28.04 


7.38 


29 




30 


29.11 


7.26 


29.08 


7.38 


29.04 


7.51 


29.01 


7.64 


30 




31 


30.08 


7.50 


30.05 


7.63 


30.01 


7.76 


29.98 


7.89 


31 




32 


31.05 


7.74 


31.02 


7.88 


30.98 


8.01 


30.95 


0.15 


32 




33 


32.02 


7.98 


31.98 


8.12 


31.95 


8.26 


31.91 


8.40 


33 




34 


32.99 


8.23 


32.95 


8.37 


32.92 


8.51 


32.88 


8.66 


34 




35 


33.96 


8.47 


33.92 


8.62 


33.89 


8.76 


33.85 


8.91 


35 




36 


34.93 


8.71 


34.89 


8.86 


34.85 


9.01 


34.81 


9.17 


36 




37 


35.90 


8.95 


35.86 


9.11 


35.82 


9. 20 


35.78 


9.42 


37 


, 


38 


36.87 


9.19 


36.83 


9.35 


36.79 


9.51 


36.75 


9.67 


38 




39 


37.84 


9.44 


37.80 


9.60 


37.76 


9.76 


37.71 


9.93 


39 




40 


38.81 


9.68 


38.77 


9.85 


38.73 


10.02 


38.68 


10.18 


40 




41 


39.73 


9.92 


39.74 


10.09 


39.69 


10.27 


39.65 


10.44 


41 




42 


40.75 


10.16 


40.71 


10.34 


40.66 


10.52 


40.62 


10.69 


42 




43 


41.72 


10.40 


41.68 


10.58 


41.63 


10.77 


41.58 


10.95 


43 




44 


42.69 


10.64 


42.65 


10.83 


42.60 


11.02 


42.55 


11.20 


44 




45 


43.66 


10.89 


43.62 


11.08 


43.57 


11.27 


43.52 


11.46 


45 




46 


44.63 


11.13 


44.58 


11.32 


44.53 


11.52 


44.48 


11.71 


46 




47 


45.60 


11.37 


45.55 


11.57 


45.50 


11.77 


45.45 


11.97 


47 




48 


46.57 


11.61 


46.52 


11.82 


46.47 


12.02 


46.42 


12.22 


48 




49 


47.54 


11.85 


47.49 


12.06 


47.44 


12.27 


47.39 


12.48 


49 




50 


48.51 


12.10 


48.46 


12.31 


48.41 


12.52 


48.35 


12.73 


50 




a 
a 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. ! 


Dep. i 
75i 


Lat. 1 g 




76 I 


**• 


75| Deg. 


75J 


Deg. j 


Deg. 


S 





TRAVERSE TABLE 



31 





3 


14 Deg. 


14i Deg. 


HI Deg. 


14} Deg. 


i 

o 

§" 

o 

CO 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


49.49 


12.34 


49.43 


12.55 


49.38 


12.77 


49.32 


12.98 


51 


52 


50.46 


12.58 


50.40 


12.80 


50.34 


13.02 


50.29 


13.24 


52 


53 


51.43 


12.82 


51.37 


13.05 


51.31 


13.27 


51.25 


13.49 


53 


54 


52.40 


13.06 


52.34 


13.29 


52.28 


13.52 


52.22 


13.75 


54 


55 


53.37 


13.31 


53.31 


13.54 


53.25 


13.77 


53.19 


14.00 


55 


56 


54.34 


13.55 


54.28 


13.78 


54.22 


14.02 


54.15 


14.26 


56 


57 


55.31 


13.79 


55.25 


14.03 


55.18 


14.27 


55.12 


14.51 


57 


58 


56.28 


14.03 


56.22 


14.28 


56.15 


14.52 


56.09 


14.77 


58 


: 59 


57.25 


14.27 


57.18 


14.52 


57.12 


14.77 


57.06 


15.02 


59 


i 60 


58.22 


14.52 


58.15 


14.77 


58.09 


15.02 


58.02 


15.28 


60 


' 61 


59.19 


14.76 


59.12 


15.02 


59.06 


15.27 


58.99 


15.53 


61 


: 62 


60.16 


V5.00 


60.09 


15.26 


60.03 


15.52 


59.96 


15.79 


62 


63 


61.13 


15.24 


61.06 


15.51 


60.99 


15.77 


60.92 


16.04 


63 


64 


62.10 


15.48 


62.03 


15.75 


61.96 


16.02 


61.89 


16.29 


64 


65 


63.07 


15.72 


63.00 


16.00 


62.93 


16.27 


62.86 


16.55 


65 ' 


66 


64.04 


15.97 


63.97 


16.25 


63.90 


16.53 


63.83 


16.80 


66 ' 


67 


65.01 


16.21 


64.94 


16.49 


64.87 


16.78 


64.79 


17.06 


67 


68 


65.98 


16.45 


65.91 


16.74 


65.83 


17.03 


65.76 


17.31 


68 


69 


66.95 


16.69 


66.88 


16.98 


66.80 


17.28 


66.73 


17.57 


69 


I 70 


67.92 


16.93 


67.85 


17.23 


67.77 


17.53 


67.69 


17.82 70 


: 71 


68.89 


17.18 


68.82 


17.48 


68.74 


17.78 


68.66 


18.08 


71 


' 72 


69.86 


17.42 


69.78 


17.72 


69.71 


18.03 


69.63 


18.33 


72 


73 


70.83 


17.66 


70.75 


17.97 


70.67 


18.28 


70.59 


18.59 


73 


74 


71.80 


17.90 


71.72 


18.22 


71.64 


18.53 


71.56 


18.84 


74 


75 


72.77 


18.14 


72.69 


18.46 


72.61 


18.78 


72.53 


19.10 


75 


76 


73.74 


18.39 


73.66 


18.71 


73.58 


19.03 


73.50 


19.35 


76 


77 


74.71 


18.63 


74.63 


18.95 


74.55 


19.28 


74.46 


19.60 


77 


78 


75.68 


18.87 


75.60 


19.20 


75.52 


19.53 


75.43 


19.86 


78 


79 


76.65 


19.11 


76.57 


19.45 


76.48 


19.78 


76.40 


20.11 


79 


80 


77.62 


19.35 


77.54 


19.69 


77.45 


20.03 


77.36 


20.37 


80 


81 


78.59 


19.60 


78.51 


19.94 


78.42 


20.28 


78.33 


20.62 


81 


82 


79.56 


19.84 


79.48 


20.18 


79.39 


20.53 


79.30 


20.88 


82 


83 


80.53 


20.08 


80.45 


20.43 


80.36 


20.78 


80.26 


21.13 


83 


84 


81.50 


20.32 


81.42 


20.68 


81.32 


21.03 


81.23 


21.39 


84 


85 


82.48 


20.56 


82.38 


20.92 


82.29 


21.28 


82.20 


21.64 


85 


86 


83.45 


20.81 


83.35 


21.17 


83.26 


21.53 


83.17 


21.90 


86 


87 


84.42 


21.05 


84.32 


21.42 


84.23 


21.78 


84.13 


22.15 


87 


88 


85.39 


21.29 


85.29 


21.66 


85.20 


22.03 


85.10 


22.41 


88 


89 


86.36 


21.53 


86.26 


21.91 


86.17 


22.28 


86.07 


22.66 


89 


90 


87.33 


21.77 


87.23 


22.15 


87.13 


22.53 


87.03 


22.91 


90 


91 


88.30 


22.01 


88.20 


22.40 


88.10 


22.78 


88.00 


23.17 


91 


92 


89.27 


22.26 


89.17 


22.65 


89.07 


23.04 


88.97 


23.42 


92 


93 


90.24 


22.50 


90.14 


22.89 


90.04 


23.29 


89.94 


23.68 


93 ' 


94 


91.21 


22.74 


91.11 


23.14 


91.01 


23.54 


90.90 


23.93 


94 


95 


92.18 


22.98 


92.08 


23.38 


91.97 


23.79 


91.87 


24.19 


95 


96 


93.15 


23.22 


93.05 


23.63 


92.94 


24.04 


92.84 


24.44 


96 


97 


94.12 


23.47 


94.02 


23.88 


93.91 


24.29 


93.80 


24.70 


97 ' 


98 


95.09 


23.71 


94.98 


24.12 


94.88 


24.54 


94.77 


24.95 


98 


99 


96.06 


23.95 


95.95 


24.37 


95.85 


24.79 


95.74 


25.21 


99 


100. 


97.03 


24.19 


96.92 


24.62 


96.81 


25.04 


96.70 


25.46 


100 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 
Q 


76 Deg. 


75| Deg. 


75* 


Deg. 


75} 


Deg. 



32 



TRAVERSE TABLE. 



g 

ST 
a 

CD 


15 


Deg. 


15* 


Deg. 


15i 


Deg. 


15| Deg. 


b 

s 
o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.97 


0.26 


0.96 


0.26 


0.96 


0.27 


0.96 


0.27 


1 


2 


1.93 


0.52 


1.93 


0.53 


1.93 


0.53 


1.92 


0.54 


2 


3 


2.90 


0.78 


2.89 


0.79 


2.89 


0.80 


2.89 


0.81 


3 


4 


3.86 


1.04 


3.86 


1.05 


3.85 


1.07 


3.85 


1.09 


4 


5 


4.83 


1.29 


4.82 


1.32 


4.82 


1.34 


4.81 


1.36 


5 


6 


5.80 


1.55 


5.79 


1.58 


5.78 


1.60 


5.77 


1.63 


6 


7 


6.76 


1.81 


6.75 


1.84 


6.75 


1.87 


6.74 


1.90 


" 


8 


7.73 


2.07 


7.72 


2.10 


7.71 


2.14 


7.70 


2.17 


8 


9 


8.69 


2.33 


8.68 


2.37 


8.67 


2.41 


8.66 


2.44 


9 


10 


9.66 


2.59 


9.65 


2.63 


9.64 


2.67 


9.62 


2.71 


10 


11 


10.63 


2.85 


10.61 


2.89 


10.60 


2.94 


10.59 


2.99 


11 


12 


11.59 


3.11 


11.58 


3.16 


11.56 


3.21 


11.55 


3.26 


12 


13 


12.56 


3.36 


12.54 


3.42 


12.53 


3.47 


12.51 


3.53 


13 


14 


13.52 


3.62 


13.51 


3.68 


13.49 


3.74 


13.47 


3.80 


14 


15 


14.49 


3.88 


14.47 


3.95 


14.45 


4.01 


14.44 


4.07 


15 


16 


15.45 


4.14 


15.44 


4.21 


15.42 


4.28 


15.40 


4.34 


16 


17 


16.42 


4.40 


16.40 


4.47 


16.38 


4.54 


16.36 


4.61 


17 


18 


17.39 


4.66 


17.37 


4.73 


17.35 


4.81 


17.32 


4.89 


18 


19 


18.35 


4.92 


18.33 


5.00 


18.31 


5.08 


18.29 


5.16 


19 


20 


19.32 


5.18 


19.30 


5.26 


19.27 


5.34 


19.25 


5.43 


20 


21 


20.28 


5.44 


20.26 


5.52 


20.24 


5.61 


20.21 


5.70 


21 


22 


21.25 


5.69 


21.23 


5.79 


21.20 


5.88 


21.17 


5.97 


22 


23 


22.22 


5.95 


22 19 


6.05 


22.16 


6.15 


22.14 


6.24 


23 


24 


23.18 


6.21 


23.15 


6.31 


23.13 


6.41 


23.10 


6.51 


24 


25 


24.15 


6.47 


24.12 


6.58 


24.09 


6.68 


24.06 


6.79 


25 


26 


25.11 


6.73 


25.08 


6.84 


25.05 


6.95 


25.02 


7.06 


26 


27 


26.08 


6.99 


26.05 


7.10 


26.02 


7.22 


25.99 


7.33 


27 


28 


27.05 


7.25 


27.01 


7.36 


26.98 


7.48 


26.95 


7.60 


28 


29 


28.01 


7.51 


27.98 


7.63 


27.95 


7.75 


27.91 


7.87 


29 


30 


28.98 


7.76 


28.94 


7.89 


28.91 


8.02 


28.87 


8.14 


30 


31 


29.94 


8.02 


29.91 


8.15 


29.87 


8.28 


29.84 


8.41 


31 


32 


30.91 


8. £8 


30.87 


8.42 


30.84 


8.55 


30.80 


8.69 


32 


33 


31.88 


8.54 


31.84 


8.68 


31.80 


8.82 


31.76 


8.96 


33 


34 


32.84 


8.80 


32.80 


8.94 


32.76 


9.09 


32.72 


9.23 


34 


35 


33.81 


9.06 


33.77 


9.21 


33.73 


9.35 


33.69 


9.50 


35 


36 


34.77 


9.32 


34.73 


9.47 


34.69 


9.62 


34.65 


9.77 


36 


37 


35.74 


9.58 


35.70 


9.73 


35.65 


9.89 


35.61 


10.04 


37 


38 


36.71 


9.84 


36.66 


10.00 


36.62 


10.16 


36.57 


10.31 


3:; 


39 


37.67 


10.09 


37.63 


10.26 


37.58 


10.42 


37.54 


10.59 


39 


40 


38.64 


10.35 


38.59 


10.52 


38.55 


10.69 


38.50 


10.86 


40 


41 


39.60 


10.61 


39.56 


10.78 


39.51 


10.96 


39.46 


11.13 


41 


42 


40.57 


10.87 


40.52 


11.05 


40.47 


11.22 


40.42 


11.40 


42 


43 


41.53 


11.13 


41.49 


11.31 


41.44 


11.49 


41.39 


11.67 


43 


44 


42.50 


11.39 


42.45 


11.57 


42.40 


11.76 


42.35 


11.94 


44 


45 


43.47 


11.65 


43.42 


11.84 


43.36 


12.03 


43.31 


12.21 


45 


46 


44.43 


11.91 


44.38 


12.10 


44.33 


12.29 


44.27 


12.49 1 46 


47 


45.40 


12.16 


45.35 


12.36 


45.29 


12.56 


45.24 


12.76 


47 


48 


46.36 


12.42 


46.31 


12.63 


46.25 


12.83 


46.20 


13.03 


48 


49 


47.33 


12.68 


47.27 


12.89 


47.22 


13.09 


47.16 


13.30 


49 


50 


48.30 


12.94 


48.24 


13.15 


48.18 


13.36 


48.12 


13.57 


50 


Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

a 

5 


75 


Deg. 


74| 


Deg. 


74* Deg. 


74i 


Deg. 



TRAVERSE TABLE. 



33 



g 
1 

a 
? 


15 Deg. 


15* Deg. 


15i Deg. 


15| Deg. 


i 

3 
o 
ffi 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


49.26 


13.20 


49.20 


13.41 


49.15 


13.63 


49.09 


13.84 


51 


52 


50.23 


13.46 


50.17 


13.68 


50.11 


13.90 


50.05 


14.11 


52 


53 


51.19 


13.72 


51.13 


13.94 


51.07 


14.16 


51.01 


14.39 


53 


54 


52.16 


13.98 


52.10 


14.20 


52.04 


14.43 


51.97 


14.66 


54 


55 


53.13 


14.24 


53.06 


14.47 


53.00 


14.70 


52.94 


14.93 


55 


56 


54.09 


14.49 


54.03 


14.73 


53.96 


14.97 


53.90 


15.20 


56 


57 


55.06 


14.75 


54.99 


14.99 


54.93 


15.23 


54.86 


15.47 


57 


58 


56.02 


15.01 


55.96 


15.26 


55.89 


15.50 


55.82 


15.74 


58 ■ 


59 


56.99 


15.27 


56.92 


15.52 


56.85 


15.77 


56.78 


16.01 


59 


60 


57.96 


15.53 


57.89 


15.78 


57.82 


16.03 


57.75 i 16.29 


60 


61 


58.92 


15.79 


58.85 


16.04 


58.78 


16.30 


58.71 


16.56 


61 


62 


59.89 


16.05 


59.82 


16.31 


59.75 


16.57 


59.67 


16.83 


62 


63 


60.85 


16.31 


60.78 


16.57 


60.71 


16.84 


60.63 


17.10 


63 


64 


61.82 


16.56 


61.75 


16.83 


61.67 


17.10 


61.60 


17.37 


64 


65 


62.79 


16.82 


62.71 


17.10 


62.64 


17.37 


62.56 


17.64 


65 


66 


63.75 


17.08 


63.68 


17.36 


63.60 


17.64 


63.52 


17.92 


66 


67 


64.72 


17.34 


64.64 


17.62 


64.56 


17.90 


64.48 


18.19 


67 


68 


65.68 


17.60 


65.61 


17.89 


65.53 


18.17 


65.45 


18.46 


68 


69 


66.65 


17.86 


66.57 


18.15 


66.49 


18.44 


66.41 


18.73 


69 


70 


67.61 


18.12 


67.54 


18.41 


67.45 


18.71 


67.37 


19.00 


70 


71 


68.58 


18.38 


68.50 


18.68 


68.42 


18.97 


68.33 


19.27 


71 


72 


69.55 


18.63 


69.46 


18.94 


69.38 


19.24 


69.30 


19.54 


72 


73 


70.51 


18.89 


70.43 


19.20 


70.35 


19.51 


70.26 


19.82 


73 


74 


71.48 


19.15 


71.39 


19.46 


71.31 


19.78 


71.22 


20.09 


74 


75 


72.44 


19.41 


72.36 


19.73 


72.27 


20.04 


72.18 


20.36 


75 


76 


73.41 


19.67 


73.32 


19.99 


73.24 


20.31 


73.15 


20.63 


76 


77 


74.38 


19.93 


74.29 


20.25 


74.20 


20.58 


74.11 


20.90 


77 


78 


75.34 


20.19 


75.25 


20.52 


75.16 


20.84 


75.07 


21.17 


78 


79 


76.31 


20.45 


76.22 


20.78 


76.13 


21.11 


76.03 


21.44 


79 


80 


77.27 


20.71 


77.18 


21.04 


77.09 


21.38 


77.00 


21.72 


80 


81 


78.24 


20.96 


78.15 


21.31 


78.05 


21.65 


77.96 


21.99 


81 


82 


79.21 


21.22 


79.11 


21.57 


79.02 


21.91 


78.92 


22.26 


82 


83 


80.17 


21.48 


80.08 


21.83 


79.98 


22.18 


79.88 


22.53 


83 


84 


81.14 


21.74 


81.04 


22.09 


80.94 


22.45 


80.85 


22.80 


84 


85 


82.10 


22.00 


82.01 


22.36 


81.91 


22.72 


81.81 


23.07 


85 


86 


83.07 


22.26 


82.97 


22.62 


82.87 


22.98 


82.77 


23.34 


86 


87 


84.04 


22.52 


83.94 


22.88 


83.84 


23.25 


83.73 


23.62 


87 


88 


85.00 


22.78 


84.90 


23.15 


84.80 


23.52 


84.70 


23.89 


88 


89 


85.97 


23.03 


85.87 


23.41 


85.76 


23.78 


85.66 


24.16 


89 


90 


86.93 


23.29 


86.83 


23.67 


86.73 


24.05 


86.62 


24.43 


90 


91 


87.90 


23.55 


87.80 


23.94 


87.69 


24.32 


87.58 


24.70 


91 


92 


88.87 


23.81 


88.76 


24.20 


88.65 


24.59 


88.55 


24.97 


92 


93 


89.83 


24.07 


89.73 


24.46 


89.62 


24.85 


89.51 


25.24 


93 


94 


90.80 


24.33 


90.69 


24.72 


90.58 


25.12 


90.47 


25.52 


94 


95 


91.76 


24.59 


91.65 


24.99 


91.54 


25.39 


91.43 


25.79 


95 


96 


92.73 


24.85 


92.62 


25.25 


92.51 


25.65 


92.40 


26.06 


96 


97 


93.69 


25.11 


93.58 


25. ol 


93.47 


25.92 


93.36 


26.33 


97 
98 


98 


94.66 


25.36 


94.55 


25.78 


94.44 


26.19 


94.32 


26.60 


99 


95.63 


25.62 


95.51 


26.04 


95.40 


26.46 


95.28 


26.87 


99 


100 


96.59 


25.88 


96.48 


26.30 


96.36 


26.72 


96.25 


27.14 


100 


a 

o 

5 
1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

a 

3 


75 1 


>eg. 


74| Deg. 


74i 


D* , 


74i Deg. 



27 



2R 



34 



TRAVERSE TABLE. 



3 
O 


16 Deg. 


16i Deg. 


16i Deg. 


16J Deg. 


D 

1 
o 
a 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


0.96 


0.28 


0.96 


0.28 


0.96 


0.28 


0.96 


0.29 


j 




2 


1.92 


0.55 


1.92 


0.56 


1.92 


0.57 


1.92 


0.58 


2 




3 


2.88 


0.83 


2.88 


0.84 


2.88 


0.85 


2.87 


0.86 


3 




4 


3.85 


1.10 


3.84 


1.12 


3.84 


1.14 


3.83 


1.15 


4 




5 


4.81 


1.38 


4.80 


1.40 


4.79 


1.42 


4.79 


1.44 


5 




6 


5.77 


1.65 


5.76 


1.68 


5.75 


1.70 


5.75 


1.73 


6 




7 


6.73 


1.93 


6.72 


1.96 


6.71 


1.99 


6.70 


2.02 


7 




8 


7.69 


2.21 


7.68 


2.24 


7.67 


2.27 


7.66 


2.31 


8 




9 


8.65 


2.48 


8.64 


2.52 


8.63 


2.56 


8.62 


2.59 


9 




10 


9.61 


2.76 


9.60 


2.80 


9.59 


2.84 


9.58 


2.88 


10 




11 


10.57 


3.03 


10.56 


3.08 


10.55 


3.12 


10.53 


3.17 


11 




12 


11.54 


3.31 


11.52 


3.36 


11.51 


3.41 


11.49 


3.46 


12 




13 


12.50 


3.58 


12.48 


3.64 


12.46 


3.69 


12.45 


3.75 


13 




14 


13.46 


3.86 


13.44 


3.92 


13.42 


3.98 


13.41 


4.03 


14 




15 


14.42 


4.13 


14.40 


4.20 


14.38 


4.26 


14.36 


4.32 


15 




16 


15.38 


4.41 


15.36 


4.48 


15.34 


4.54 


15.32 


4.61 


16 




17 


16.34 


4.69 


16.32 


4.76 


16.30 


4.83 


16.28 


4.90 


17 




18 


17.30 


4.96 


17.28 


5.04 


17.26 


5.11 


17.24 


5.19 


18 




19 


18.26 


5.24 


18.24 


5.32 


18.22 


5.40 


18.19 


5.48 


19 




20 


19.23 


5.51 


19.20 


5.60 


19.18 


5.68 


19.15 


5.76 


20 




21 


20.19 


5.79 


20.16 


5.88 


20.14 


5.96 


20.11 


6.05 


21 




22 


21.15 


6.06 


21.12 


6.16 


21.09 


6.25 


21.07 


6.34 


22 




23 


22.11 


6.34 


22.08 


6.44 


22.05 


6.53 


22.02 


6.63 


23 




24 


23.07 


6.62 


23.04 


6.72 


23.01 


6.82 


22.98 


6.92 


24 




25 


24.03 


6.89 


24.00 


7.00 


23.97 


7.10 


23.94 


7.20 


25 




26 


24.99 


7.17 


24.96 


7.28 


24.93 


7.38 


24.90 


7.49 


26 




27 


25.95 


7.44 


25.92 


7.56 


25.89 


7.67 


25.85 


7.78 


27 




28 


26.92 


7.72 


26.88 


7.84 


26.85 


7.95 


26.81 


8.07 


28 




29 


27.88 


7.99 


27.84 


8.11 


27.81 


8.24 


27.77 


8.36 


29 




30 


28.84 


8.27 


28.80 


8.39 


28.76 


8.52 


28.73 


8.65 


30 




31 


29.80 


8.54 


29.76 


8.67 


29.72 


8.80 


29.08 


8.93 


31 




32 


30.76 


8.82 


30.72 


8.95 


30.68 


9.09 


30.64 


9.22 


32 




33 


31.72 


9.10 


31.68 


9.23 


31.64 


9.37 


31.60 


9.51 


33 




34 


32.68 


9.37 


32.64 


9.51 


32.60 


9.66 


32-56 


> 9.80 


34 




35 


33.64 


9.65 


33.60 


9.79 


33.56 


9.94 


33.51 


10.09 


35 




36 


34.61 


9.92 


34.56 


10.07 


34.52 


10.22 


34.47 


10.38 


36 




37 


35.57 


10.20 


35.52 


10.35 


35.48 


10.51 


35.43 


10.66 


37 




38 


36.53 


10.47 


36.48 


10.63 


36.44 


10.79 


36.39 


10.95 


38 




39 


37.49 


10.75 


37.44 


10.91 


37.39 


11.08 


37.35 


11.24 


39 




40 


38.45 


11.03 


38.40 


11.19 


38.35 


11.36 


38.30 


11.53 


40 




41 


39.41 


11.30 


39.36 


11.47 


39.31 


11.64 


39.26 


11.82 


41 




42 


40.37 


11.58 


40.32 


11.75 


40.27 


11.93 


40.22 


12.10 


42 




43 


41.33 


11.85 


41.28 


12.03 


41.23 


12.21 


41.18 


12.39 


43 




44 


42.30 


12.13 


42.24 


12.31 


42.19 


12-50 


42.13 


12.68 


44 




45 


43.26 


12.40 


43.20 


12.59 


43.15 


12.78 


43.09 


12.97 


45 




46 


44.22 


12.68 


44.16 


12.87 


44.11 


13.06 


44.05 


13.26 






47 


45.18 


12.95 


45.12 


13.15 


45.06 


13.35 


45.01 


13.55 


47 




j 48 


46.14 


13.23 


46.08 


13.43 


46.02 


13.63 


45.96 


13.83 






49 


47.10 


13.51 


47.04 


13.71 


46.93 


13.92 


46.92 


14.12 


49 




50 


48.06 


13.78 


48.00 


13.99 


47.94 


14.20 


47.88 


14.41 


50 




o 

a 
fj 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. | 


Lat. 


ai ! 

1 ' 




74 1 


)eg. 


73| 


- 


73J 


Deg. 


73* 


Deg. 





TRAVERSE TABLE. 



35 



c 

p 

o 
ffl 


16 Deg. 


164 Deg. 


16J Deg. 


16| Veg. 


1 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


49.02 


14.06 


48.96 


14.27 


48.90 


14.48 


48.84 


14.70 


51 


52 


49.99 


14.33 


49.92 


14.55 


49.86 


14.77 


49.79 


14.99 


52 


53 


50.95 


14.61 


50.88 


14.83 


50.82 


15.05 


50.75 


15.27 


53 ■ 


54 


51.91 


14.88 


51.84 


15.11 


51.78 


15.34 


51.71 


15.56 


54 


55 


52.87 


15.16 


52.80 


15.39 


52.74 


15.62 


52.67 


15.85 


55 


56 


53.83 


15.44 


53.76 


15.67 


53.69 


15.90 


53.62 


16.14 


56 


' 57 


54.79 


15.71 


54.72 


15.95 


54.65 


16.19 


54.58 


16.43 


57 


58 


55.75 


15.99 


55.68 


16.23 


55.61 


16.47 


55.54 


16.72 


58 


59 


56.71 


16.26 


56.64 


16.51 


56.57 


16.76 


56.50 


17.00 


59 


60 


57.68 


16.54 


57.60 


16.79 


57.53 


17.04 


57.45 


17.29 


60 


61 


58.64 


16.81 


58.56 


17.07 


58.49 


17.32 


58.41 


17.58 


61 


62 


59.60 


17.09 


59.52 


17.35 


59.45 


17.61 


59.37 


17.87 


62 


63 


60.56 


17.37 


60.48 


17.63 


60.41 


17.89 


60 33 


18.16 


63 


64 


61.52 


17.64 


61.44 


17.91 


61.36 


18.18 


61.28 


18.44 


64 


65 


62.48 


17.92 


62.40 


18.19 


62.32 


18.46 


62.24 


18.73 65 


66 


63.44 


18.19 


63.36 


18.47 


63.28 


18.74 


63.20 


19.02 66 


67 


64.40 


18.47 


64.32 


18.75 


64.24 


19.03 


64.16 


19.31 j 67 


63 


65.37 


18.74 


65.28 


19.03 


65.20 


19.31 


65.11 


19.60 


68 


69 


66.33 


19.02 


66.24 


19.31 


66.16 


19.60 


66.07 


19.89 


69 


70 


67.29 


19.29 


67.20 


19.59 


67.12 


19.88 


67.03 


20.17 


70 


71 


68.25 


19.57 


68.16 


19.87 


68.08 


20.17 


67.99 


20.46 


71 


72 


69.21 


19.85 


69.12 


20.15 


69.03 


20.45 


68.95 


20.75 


72 


73 


70.17 


20.12 


70.08 


20.43 


69.99 


20.73 


69.90 


21.04 


73 


74 


71.13 


20.40 


71.04 


20.71 


70.95 


21.02 


70.86 


21.33 


74 


75 


72.09 


20.67 


72.00 


20.99 


71.91 


21.30 


71.82 


21.61 


75 


76 


73.06 


20.95 


72.96 


21.27 


72.87 


21.59 


72.78 


21.90 


76 


77 


74.02 


21.22 


73.92 


21.55 


73.83 


21.87 


73.73 


22.19 


77 


78 


74.98 


21.50 


74.88 


21.83 


74.79 


22.15 


74.69 


22.48 


78 


79 


75.94 


21.78 


75.84 


22.11 


75.75 


22.44 


75.65 


22.77 


79 


80 


76.90 


22.05 


76.80 


22.39 


76.71 


22.72 


76.61 


23.06 


80 


81 


77.86 


22.33 


77.76 


22.67 


77.66 


23.01 


77.56 


23.34 


81 


82 


78.82 


22.60 


78.72 


22.95 


78.62 


23.29 


78.52 


23.63 


82 . 


83 


79.78 


22.88 


79.68 


23.23 


79.58 


23.57 


79.48 


23.92 


83 


84 


80.75 


23.15 


80.64 


23.51 


80.54 


23.86 


80.44 


24.21 


84 


85 


81.71 


23.43 


81.60 


23.79 


81.50 


24.14 


81.39 


24.50 


85 


86 


82.67 


23.70 


82.56 


24.07 


82.46 


24.43 


82.35 


24.78 


86 


87 


83.63 


23.98 


83.52 


24.35 


83.42 


24.71 


83.31 


25.07 


87 


88 


84.59 


24.26 


84.48 


24.62 


84.38 


24.99 


84.27 


25.36 


88 


89 


85.55 


24.53 


85.44 


24.90 


85.33 


25.28 


85.22 


25.65 


89 


90 


86.51 


24.81 


86.40 


25.18 


86.29 


25.56 


86.18 


25.94 


90 


91 


87.47 


25.08 


87.36 


25.46 


87.25 


25.85 


87.14 


26.23 


91 


92 


88.44 


25.36 


88.32 


25.74 


88.21 


26.13 


88.10 


26.51 


92 


93 


89.40 


25.63 


89.28 


26.02 


89.17 


26.41 


89.05 


26.80 


93 ! 


94 


90.36 


25.91 


90.24 


26.30 


90.13 


26.70 


90.01 


27.09 


94 


95 


91.32 


26.19 


91.20 


26.58 


91.09 


26.98 


90.97 


27.38 


95 


96 


92.28 


26.46 


92.16 


26.86 


92.05 


27.27 


91.93 


27.67 


96 


97 


93.24 


26.74 


93.12 


27.14 


93.01 


27.55 


92.88 


27.95 


97 


98 


94.20 


27.01 


94.08 


27.42 


93.96 


27.83 


93.84 


28.24 


98 


99 


95.16 


27.29 


95.04 


27.70 


94.92 


28.12 


94.80 


28.53 


99 


100 


96.13 


27.56 


96.00 


27.98 


95.88 


28.40 


95.76 


28.82 


100 


1 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


.3 

Q 


74 Deg. 


73| Deg. 


73i Deg. 


734 Deg. 



35 



TRAVERSE TABLE. 



q 

• g 

? 


17 Deg. 


I7i Deg. 


m 


Deg. 


17* Deg. 


H 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 
0.30 


1 


0.96 


0.29 


0.95 


0.30 


0.95 


0.30 


0.95 


2 


1.91 


0.58 


1.91 


0.59 


1.91 


0.60 


1.90 


0.61 


2 


3 


2.87 


0.88 


2.87 


0.89 


2.86 


0.90 


2.86 


0.91 


3 


4 


3.83 


1.17 


3.82 


1.19 


3.81 


1.20 


3.81 


1.22 


4 


5 


4.78 


1.46 


4.78 


1.48 


4.77 


1.50 


4.76 


1.52 


5 


6 


5.74 


1.75 


5.73 


1.78 


5.72 


1.80 


5.71 


1.83 


6 


7 


6.69 


2.05 


6.69 


2.08 


6.68 


2.10 


6.67 


2.13 


7 


8 


7.65 


2.34 


7.64 


2.37 


7.63 


2.41 


7.62 


2.44 


8 


9 


8.61 


2.63 


8.60 


2.67 


8.58 


2.71 


8.57 


2.74 


9 


10 


9.56 


2.92 


9.55 


2.97 


9.54 


3.01 


9.52 


3.05 


10 


11 


10.52 


3.22 


10.51 


3.26 


10.49 


3.31 


10.48 


3.35 


11 


12 


11.48 


3.51 


11.46 


3.56 


11.44 


3.61 


11.43 


3.66 


12 


13 


12.43 


3.80 


12.42 


3.85 


12.40 


3.91 


12.38 


3.96 


13 


14 


13.39 


4.09 


13.37 


4.15 


13.35 


4.21 


13.33 


4.27 


14 


15 


14.34 


4.39 


14.33 


4.45 


14.31 


4.51 


14.29 


4.57 


15 


16 


15.30 


4.68 


15.28 


4.74 


15.26 


4.81 


15.24 


4.88 


16 


17 


16.26 


4.97 


16.24 


5.04 


16.21 


5.11 


16.19 


5.18 


17 


18 


17.21 


5.26 


17.19 


5.34 


17.17 


5.41 


r.14 


5.49 


18 


19 


18.17 


5.56 


18.15 


5.63 


18.12 


5.71 


18.10 


5.79 


19 


20 


19.13 


5.85 


19.10 


5.93 


19.07 


6.01 


19.05 


6.10 


20 


21 


20.08 


6.14 


20.06 


6.23 


20.03 


6.31 


20.00 


6.40 


21 


22 


21.04 


6.43 


21.01 


6.52 


20.98 


6.62 


20.95 


6.71 


22 


23 


21.99 


6.72 


21.97 


6.82 


21.94 


6.92 


21.91 


7.01 


23 


24 


22.95 


7.02 


22.92 


7.12 


22.89 


7.22 


1 22.86 


7.32 


24 


25 


23.91 


7.31 


23.88 


7.41 


23.84 


7.52 


23.81 


7.62 


25 


26 


24.86 


7.60 


24.83 


7.71 


24.80 


7.82 


24.76 


7.93 


26 


27 


25.82 


7.89 


25.79 


8.01 


25.75 


8.12 


25.71 


8.23 


27 


28 


26.78 


8.19 


26.74 


8.30 


26.70 


8.42 


26.67 


8.54 


28 


29 


27.73 


8.48 


27.70 


8.60 


27.66 


8.72 


27.62 


8.84 


29 


30 


28.69 


8.77 


28.65 


8.90 


28.61 


9.02 


28.57 


9.15 


30 


31 


29.65 


9.06 


29.61 


9.19 


29.57 


9.32 


29.52 


9.45 


31 


32 


30.60 


9.36 


30.56 


9.49 


30.52 


9.62 


30.48 


9.76 


32 


33 


31.56 


9.65 


31.52 


9.79 


31.47 


9.92 


31.43 


10.06 


33 


34 


32.51 


9.94 


32.47 


10.08 


32.43 


10.22 


32.38 


10.37 


34 


35 


33.47 


10.23 


33.43 


10.38 


33.38 


10.52 


33.33 


10.67 


35 


36 


34.43 


10.53 


34.38 


10.68 


34.33 


10.83 


34.29 


10.98 


36 


37 


35.38 


10.82 


35.34 


10.97 


35.29 


11.13 


35.24 


11.28 


37 


38 


36.34 


11.11 


36.29 


11.27 


36.24 


11.43 


36.19 


11.58 


38 


39 


37.30 


11.40 


37.25 


11.57 


37.19 


11.73 


37.14 


11.89 


39 


40 


38.25 


11.69 


38.20 


11.86 


38.15 


12.03 


38.10 


12.19 


40 


41 


39.21 


11.99 


39.16 


12.16 


39.10 


12.33 


39.05 


12.50 


41 


42 


40.16 


12.28 


40.11 


12.45 


40.06 


12.63 


40.00 


12.80 


42 


43 


41.12 


12.57 


41.07 


12.75 


41.01 


12.93 


40.95 


13.11 


43 


44 


42.08 


12.86 


42.02 


13.05 


41.96 


13.23 


41.91 


13.41 


44 


45 


43.03 


13.16 


42.98 


13.34 


42.92 


13.53 


42.86 


13.72 


45 


46 


43.99 


13.45 


43.93 


13.64 


43.87 


13.83 


43.81 


14.02 


46 


47 


44.95 


13.74 


44.89 


13.94 


44.82 


14.13 


44.76 


14.33 


47 


48 


45.90 


14.03 


45.84 


14.23 


45.78 


14.43 


45.71 


14.63 


48 


49 


46.86 


14.33 


46.80 


14.53 


46.73 


14.73 


46.67 


14.94 


49 


50 


47.82 


14.62 


47.75 


14.83 


47.69 


15.04 


47.62 


15.24 


50 


u 

S 


Dep. 


Lat. 


Dep. 


Lat. j 


Dep. 


Lat. 


Dep. 


Lat. 


V 

u 

e 


73 I 


)(£{ 


72J 


Deg. | 


72$ 


Deg. 


72} 


Deg. 



TRAVERSE TABLE 



37 





1 17 Deg. 


17i Deg. 


17$ Deg. 


17| Deg. 


e 

ST 
a 
? 


o 

CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


48.77 


14.91 


48.71 


15.12 


48.64 


15.34 


48.57 


15.55 


51 


52 


49.73 


15.20 


49.66 


15.42 


49.59 


15.64 


49.52 


15.85 


52 


53 


50.68 


15.50 


50.62 


15.72 


50.55 


15.94 


50.48 


16.16 


53 


54 


51.64 


15.79 


51.57 


16.01 


51.50 


16.24 


51.43 


16.46 


54 


55 


52.60 


16.08 


52.53 


16.31 


52.45 


16.54 


52.38 


16.77 


55 


56 


53.55 


16.37 


53.48 


16.61 


53.41 


16.84 


53.33 


17.07 


56 


57 


54.51 


16.67 


54.44 


16.90 


54.36 


17.14 


54.29 


17.38 


57 


58 


55.47 


16.96 


55.39 


17.20 


55.32 


17.44 


55.24 


17.68 


58 


59 


56.42 


17.25 


56.35 


17.50 


56.27 


17.74 


56.19 


17.99 


59 


60 


57.38 


17.54 


57.30 


17.79 


57.22 


18.04 


57.14 


18.29 


60 


61 | 58.33 


17.83 


58.26 


18.09 


58.18 


18.34 


58.10 


18.60 


61 


62 


59.29 


18.13 


59.21 


18.39 


59.13 


18.64 


59.05 


18.90 


62 


63 


60.25 


18.42 


60.17 


18.68 


60.08 


18.94 


60.00 


19.21 


63 


64 


61.20 


18.71 


61.12 


18.98 


61.04 


19.25 


60.95 


19.51 


64 


65 


62.16 


19.00 


62.08 


19.28 


61.99 


19.55 


61.91 


19.82 


65 


66 


63.12 


19.30 


63.03 


19.57 


62.95 


19.85 


62.86 


20.12 


66 


67 


64.07 


19.59 


63.99 


19.87 


63.90 


20.15 


63.81 


20.43 


67 


68 


65.03 


19.88 


64.94 


20.16 


64.85 


20.45 


64.76 


20.73 


68 


69 


65.99 


20.17 


65.90 


20.46 


65.81 


20.75 


65.72 


21.04 


69 


70 


66.94 


20.47 


66.85 


20.76 


66.76 


21.05 


66.67 


21.34 


70 


71 


67.90 


20.76 


67.81 


21.05 


67.71 


21.35 


67.62 


21.65 


71 


72 


68.85 


21.05 


68.76 


21.35 


68.67 


21.65 


68.57 


21.95 


72 


73 


69.81 


21.34 


69.72 


21.65 


69.62 


21.95 


69.52 


22.26 


73 


74 


70.77 


21.64 


70.67 


21.94 


70.58 


22.25 


70.48 


22.56 


74 


75 


71.72 


21.93 


71.63 


22.24 


71.53 


22.55 


71.43 


22.86 


75 


76 


72.68 


22.22 


72.58 


22.54 


72.48 


22.85 


72.38 


23.17 


76 


77 


73.64 


22.51 


73-54 


22.83 


73.44 


23.15 


73.33 


23.47 


77 


78 


74.59 


22.80 


74.49 


23.13 


74.39 


23.46 


74.29 


23.78 


78 


79 


75.55 


23.10 


75.45 


23.43 


75.34 


23.76 


75.24 


24.08 


79 


80 


76.50 


23.39 


76.40 


23.72 


76.30 


24.06 


76.19 


24.39 


80 


81 


77.46 


23.68 


77.36 


24.02 


77.25 


24.36 


77.14 


24.69 


81 


82 


78.42 


23.97 


78.31 


24.32 


78.20 


24.66 


78.10 


25.00 


82 


83 


79.37 


24.27 


79.27 


24.61 


79.16 


25.96 


79.05 


25.30 


83 


84 


80.33 


24.56 


80.22 


24.91 


80.11 


25-26 


80.00 


25.61 


84 


85 


81.29 


24.85 


81.18 


25.21 


81.07 


25.56 


80.95 


25.91 


85 


86 


82.24 


25.14 


82.13 


25.50 


82.02 


25.86 


81.91 


26.22 


86 


87 


83.20 


25.44 


83.09 


25.80 


82.97 


26.16 


82.86 


26.52 


87 


88 


84.15 


25.73 


84.04 


26.10 


83.93 


26.46 


83.81 


26.83 


88 


89 


85.11 


26.02 


85.00 


26.39 


84.88 


26.76 


84.76 


27.13 


89 


90 


86.07 


26.31 


85.95 


26.69 


85.83 


27.06 


85.72 


27.44 


no 


91 


87.02 


26.61 


86.91 


26.99 


86.79 


27.36 


86.67 


27.74 


91 


92 


87.98 


26.90 


87.86 


27.28 


87.74 


27.66 


87.62 


28.05 


92 


93 


88.94 


27.19 


88.82 


27.58 


88.70 


27.97 


88.57 


28.35 


93 


94 


89.89 


27.48 


89.77 


27.87 


89.65 


28.27 


89.53 


28.66 


94 


95 


90.85 


27.78 


90.73 


28.17 


90.60 


28.57 


90.48 


28.96 


95 


96 


91.81 


28.07 


91.68 


28.47 


91.56 


28.87 


91.43 


29.27 


96 


97 


92.76 


28.36 


92.64 


28.76 


92.51 


29.17 


92.38 


29.57 


97 


98 


93.72 


28.65 


93.59 


29.06 


93.46 


29.47 


93.33 


29.88 


98 


99 


94.67 


28.94 


94.55 


29.36 


94.42 


29.77 


94.29 


30.18 


99 


100 


95.63 


29.24 


95.50 


29.65 


95.37 


30.07 


95.24 


30.49 


100 


o 


Dep. 


Lat. 


Dep 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Q 1 


73 Deg. 

! 


72| Deg. 


72£ Deg. 


72i Deg. 



27 : 



33 



TRAVERSE TABLE. 




TRAVERSE TABLE. 



39 



o 

to 

3 
o 
? 


18 Deg. 


18i Beg. 


18i Deg. 


18| Deg. 




1 

s 
o 
n> 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


48.50 


15.76 


48.43 


15.97 


48.36 


16.18 


48.29 


16.39 


51 


52 


49.45 


16.07 


49.38 


16.28 


49.31 16.50 


49.24 


16.71 


52 


53 


50.41 


16.38 


50.33 


16.60 


50.26 


16.82 


50.19 


17.04 


53 


54 


51.36 


16.69 


51.28 


16.91 


51.21 


17.13 


51.13 


17.36 


54 


55 


52.31 


17.00 


52.23 


17.22 


52.16 


17.45 


52.08 


17.68 


55 


56 


53.26 


17.30 


53.18 


17.54 


53.11 


17.77 


53.03 


18.00 


56 


57 


54.21 


17.61 


54.13 


17.85 


54.05 


18.09 


53.98 


18.32 


57 


58 


55.16 


17.92 


55.08 


18.16 


55.00 


18.40 


54.92 


18.64 


58 


59 


56.11 


18.23 


56.03 


18.48 


55.95 


18.72 


55.87 


18.96 


59 


60 


57.06 


18.54 


56.98 


18.79 


56.90 


19.04 


56.82 


19.29 


60 


61 


58.01 


18.85 


57.93 


19.10 


57.85 


19.36 


57.76 


19.61 


61 


62 


58.97 


19.16 


58.88 


19.42 


58.80 


19.67 


58.71 


19.93 


62 


63 


59.92 


19.47 


59.83 


19.73 


59.74 


19.99 


59.66 


20.25 


63 


64 


60.87 


19.78 


60.78 


20.04 


60.69 


20.31 


60.60 


20.57 


64 


65 


61.82 


20.09 


61.73 


20.36 


61.64 


20.62 


61.55 


20.89 


65 


66 


62.77 


20.40 


62.68 


20.67 


62.59 


20.94 


62.50 


21.22 


66 


67 
68 


63.72 


20.70 


63.63 


20.98 


63.54 


21.26 


63.44 


21.54 


67 


64.67 


21.01 


64.58 


21.30 


64.49 


21.58 


64.39 


21.86 


68 


69 


65.62 


21.32 


65.53 


21.61 


65.43 


21.89 


65.34 


22.18 


69 : 


70 


66.57 


21.63 


66.48 


21.92 


66.38 


22.21 


66.29 


22.50 


70 


71 


67.53 


21.94 


67.43 


22.23 


67.33 


22.53 


67.23 


22.82 


71 


72 


68.48 


22.25 


68.38 


22.55 


68.28 


22.85 


68.18 


23.14 


72 


73 


69.43 


22.56 


69.33 


22.86 


69.23 


23.16 


69.13 


23.47 


73 


74 


70.38 


22.87 


70.28 


23.17 


70.18 


23.48 


70.07 


23.79 


74 


75 


71.33 


23.18 


71.23 


23.49 


71.12 


23.80 


71.02 


24.11 


75 


76 


72.28 


23.49 


72.18 


23.80 


72.07 


24.12 


71.97 


24.43 


76 


1 77 


73.23 


23.79 


73.13 


24.11 


73.02 


24.43 


72.91 


24.75 


77 


I 78 


74.18 


24.10 


74.08 


24.43 


73.97 


24.75 


73.86 


25.07 


78 


I 79 


75.13 


24.41 


75.03 


24.74 


74.92 


25-07 


74.81 


25.39 


79 


[ 80 


76.08 


24.72 


75.98 


25.05 


75.87 


25.38 


75.75 


25.72 


80 


1 81 


77.04 


25.03 


76.93 


25.37 


76.81 


25.70 


76.70 


26.04 


81 


1 82 


77.99 


25.34 


77.88 


25.68 


77.76 


26.02 


77.65 


26.36 


82 


83 


78.94 


25.65 


78.83 


25.99 


78.71 


26.34 


78.60 


26.68 


83 


84 


79.89 


25.96 


79.77 


26.31 


79.66 


26.65 


79.54 


27.00 


84 


85 


80.84 


26.27 


80.72 


26.62 


80.61 


26.97 


80.49 


27.32 


85 


86 


81.79 


26.58 


81.67 


26.93 


81.56 


27.29 


81.44 


27.64 


86 : 


87 


82.74 


26.88 


82.62 


27.25 


82.50 


27.61 


82.38 


27.97 


87 r 


88 


83.69 


27.19 


83.57 


27.56 


83.45 


27.92 


83.33 


28.29 


88 il 


89 


84.64 


27.50 


84.52 


27.87 


84.40 


28.24 


84.28 


28.61 


89 I 


90 


85.60 


27.81 


85.47 


28.18 


85.35 


28.56 


85.22 


28.93 


90 


91 


86.55 


28.12 


86.42 


28.50 


86.30 


28.87 


86.17 


29.25 


91 


92 


87.50 


28.43 


87.37 


28.81 


87.25 


29.19 


87.12 


29.57 


92 


93 


88.45 


28.74 


88.32 


29.12 


88.19 


29.51 


88.06 


29.89 


93 


94 


89.40 


29.05 


89.27 


29.44 


89.14 


29.83 


89.01 


30.22 


94 


95 


90.35 


29.36 


90.22 


29.75 


90.09 


30.14 


89.96 


30.54 


95 


96 


91.30 


29.67 


91:17 


30.06 


91.04 


30.46 


90.91 


30.86 


96 


97 


92.25 


29.97 


92.12 


30.38 


91.99 


30.78 


91.85 


31.18 


97 


98 


93.20 


30.28 


93.07 


30.69 


92.94 


31.10 


92.80 


31.50 


98 


99 


94.15 


30.59 


94.02 


31.00 


93.88 


31.41 


93.75 


31.82 


99 


100 


95.11 


30.90 


94.97 


31.32 


94.83 


31.73 


94.69 


32.14 


100 


6 

a 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


c 
5 


72 Beg. 


71| Deg. 


7li Deg. 


71* Deg. 



TRAVERSE TABLE 




TRAVERSE TABLE. 



41 



o 

1 

o 

CD 

51 


19 Deg. 


19£ Deg. 


19i Deg. 


191 Deg. 




2 

O 

re 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


48.22 


16.60 


48.15 


16.81 


48.07 


17.02 


48.00 


17.23 


51 


52 


49.17 


16.93 


49.09 


17.14 


49.02 


17.36 


48.94 


17.57 


52 


53 


50.11 


17.26 


50.04 


17.47 


49.96 


17.69 


49.88 


17.91 


53 


54 


51.06 


17.58 


50.98 


17.80 


50.90 


18.03 


50.82 


18.25 


54 


55 


52.00 


17.91 


51.92 


18.13 


51.85 


18.36 


51.76 


18.6b 


55 


56 


52.95 


18.23 


52.87 


18.46 


52.79 


18.69 


52.71 


18.92 ' 5S 


57 


53.89 


18.56 


53.81 


18.79 


53.73 


19.03 


53.65 


19.26 


57 


58 


54.84 


18.88 


54.76 


19.12 


54.67 


19.36 


54.59 


19.60 


58 


59 


55.79 


19.21 


55.70 


19.45 


55.62 


19.69 


55.53 


19.94 


59 


60 


56.73 


19.53 


56.65 


19.78 


56.56 


20.03 


56.47 


20.27 


60 


61 


57.68 


19.86 


57.59 


20.11 


57.50 


20.36 


57.41 


20.61 


61 ' 


62 


58.62 


20.19 


58.53 


20.44 


58.44 


20.70 


58.35 


20.95 


62 


63 


59.57 


20.51 


59.48 


20.77 


59.39 


21.03 


59.29 


21.29 


63 


64 


60.51 


20.84 


60.42 


21.10 


60.33 


21.36 


60.24 


21.63 


64 


65 


61.46 


21.16 


61.37 


21.43 


61.27 


21.70 


61.18 


21.96 


65 


66 


62.40 


21.49 


62.31 


21.76 


62.21 


22.03 


62.12 


22.30 


66 


67 


63.35 


21.81 


63.25 


22.09 


63.16 


22.37 


63.06 


22.64 


67 


68 


64 30 


22.14 


64.20 


22.42 


64.10 


22.70 


64.00 


22.98 


68 


69 


65.24 


22.46 


65.14 


22.75 


65.04 


23.03 


64.94 


23.32 


69 


70 
71 


€6 19 


22.79 


66.09 


23.08 


65.98 


23.37 


65.88 


23.65 


70 , 


67.13 


23.12 


67.03 


23.41 


66.93 


23.70 


66.82 


23.99 


71 


72 


68.08 


23.44 


67.97 


23.74 


67.87 


24.03 


67.76 


24.33 


72 


73 


69.02 


23.77 


68.92 


24.07 


68.81 


24.37 


68.71 


24.67 


73 I 


74 


69.97 


24.09 


69.86 


24.40 


69.76 


24.70 


69.65 


25.01 


74 


75 


70.91 


24.42 


70.81 


24.73 


70.70 


25.04 


70.59 


25.34 


75 ; 


76 


71.86 


24.74 


71.75 


25.06 


71.64 


25.37 


71.53 


25.68 


76 


77 


72.80 


25.07 


72-69 


25.39 


72.58 


25.70 


72.47 


26.02 


77 


78 


73.75 


25.39 


73.64 


25.72 


73.53 


26.04 


73.41 


26.36 


78 . 


79 


74.70 


25.72 


74.58 


26.05 


74.47 


26.37 


74.35 


26.70 


79 


80 


75.64 


26.05 


75.53 


26.38 


75.41 


26.70 


75.29 


27.03 


80 


81 


76.59 


26.37 


76.47 


26.70 


76.35 


27.04 


76.24 


27.37 


81 . 


82 


77.53 


26.70 


77.42 


27.03 


77.30 


27.37 


77.18 


27.71 


82 


83 


78.48 


27.02 


78.36 


27.36 


78.24 


27.71 


78.12 


28.05 


33 


84 


79.42 


27.35 


79.30 


27.69 


79.18 


28.04 


79.06 


28.39 


84 


85 


80.37 


27.67 


80.25 


28.02 


no. 12 


28.37 


80.00 


28.72 


85 


86 


81.31 


28.00 


81.19 


28.35 


81.07 


28.71 


80.94 


29.06 


86 


' 87 


82.26 


28.32 


82.14 


28.68 


82.01 


29.04 


81.88 


29.40 


87 


88 


83.21 


28.65 


83.08 


29.01 


82.95 


29.37 


82.82 


29.74 


88 


89 


84.15 


28.98 


84.02 


29.34 


83.90 


29.71 


83.76 


30.07 


89 


90 


85.10 


29.30 


84.97 


29.67 


84.84 


30.04 


84.71 


30.41 


90 ' 


91 


86.04 


29.63 


85.91 


30.00 


85.78 


30.38 


85.65 


30.75 


91 


92 


86.99 


29.95 


86.86 


30.33 


86.72 


30.71 


86.59 


31.09 


92 


93 


87.93 


30.28 


87.80 


30.66 


87.67 


31.04 


87.53 


31.43 


93 


94 


88.88 


30.60 


88.74 


30.99 


88.61 


31.38 


88.47 


31.76 


94 


95 


89.82 


30.93 


89.60 


31.32 


89.55 


31.71 


89.41 


32.10 


95 


96 


90.77 


31.25 


90.63 


31.65 


90.49 


32.05 


90.35 


32.44 


96 


97 


91.72 


31.58 


91.58 


31.98 


91.44 


32.38 


91.29 


32.78 


97 


98 


92.66 


31.91 


92.52 


32.31 


92.38 


32.71 


92.24 


33.12 


98 


99 


93.61 


32.23 


93.46 


32.64 


93.32 


33.05 


93.18 


33.45 


99 


100 


94.55 


32.56 


94.41 


32.97 


94.26 


33.38 


94.12 


33.79 


100 


6 

a 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


c 

a 


71 ] 


Deg. 


70| Deg. 


70i 


Deg. 


70i 


Deg. 



2S 



42 



TRAVERSE TABLE. 



g 

V 

o 
n 


20 Deg. 


20i Deg. 


20i Deg. 


20J Deg. 


a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.94 


0.34 


0.94 


0.35 


0.94 


0.35 


0.94 


0.35 


1 


2 


1.88 


0.68 


1.88 


0.69 


1.87 


0.70 


1.87 


0.71 


2 


3 


2.82 


1.03 


2.81 


1.04 


2.81 


1.05 


2.81 


1.06 


3 


4 


3.76 


1.37 


3.75 


1.38 


3.75 


1.40 


3.74 


1.42 


4 


5 


4.70 


1.71 


4.69 


1.73 


4.68 


1.75 


4.68 


1.77 


5 


6 


5.64 


2.05 


5.63 


2.08 


5.62 


2.10 


5.61 


2.13 


6 


7 


6.58 


2.39 


6.57 


2.42 


6.56 


2.45 


6.55 


2.48 


7 


8 


7.52 


2.74 


7.51 


2.77 


7.49 


2.80 


7.48 


2.83 


8 


9 


8.46 


3.08 


8.44 


3.12 


8.43 


3.15 


8.42 


3.19 


9 


10 


9.40 
10.34 


3.42 


9.38 


3.46 


9.37 


3.50 


9.35 


3.54 


10 


11 


3.76 


10.32 


3.81 


10.30 


3.85 


10.29 


3.90 


11 


12 


11.28 


4.10 


11.26 


4.15 


11.24 


4.20 


11.22 


4.25 


12 


13 


12.22 


4.45 


12.20 


4.50 


12.18 


4.55 


12.16 


4.61 


13 


14 


13.16 


4.79 


13.13 


4.85 


13.11 


4.90 


13.09 


4.96 


14 


15 


14.10 


5.13 


14.07 


5.19 


14.05 


5.25 


14.03 


5.31 


15 


10 


15.04 


5.47 


15.01 


5.54 


14.99 


5.60 


14 96 


5.67 


16 


17 


15.97 


5.81 


15.95 


5.88 


15.92 


5.95 


15.90 


6.02 


17 


18 


16.91 


6.16 


16.89 


6.23 


16.86 


6.30 


16.83 


6.38 


18 


19 


17.85 


6.50 


17.83 


6.58 


17.80 


6.65 


17.77 


6.73 


19 


20 


18.79 


6.84 


18.76 


6.92 


18.73 


7.00 


18.70 


7.09 


20 


21 


19.73 


7.18 


19.70 


7.27 


19.67 


7.35 


19.64 


7.44 


21 


22 


20.67 


7.52 


20.64 


7.61 


20.61 


7.70 


20.57 


7.79 


22 


23 


21.61 


7.87 


21.58 


7.96 


21.54 


8.05 


21.51 


8.15 


23 


24 


22.55 


8.21 


22.52 


8.31 


22.48 


8.40 


22.44 


8.50 


24 


25 


23.49 


8.55 


23.45 


8.65 


23.42 


8.76 


23.38 


8.86 


25 


26 


24.43 


8.89 


24.39 


9.00 


24.35 


9.11 


24.31 


9.21 


26 


27 


25.37 


9.23 


25.33 


9.35 


25.29 


9.46 


25.25 


9.57 


27 


28 


26.31 


9.58 


26.27 


9.69 


26.23 


9.81 


26.18 


9.92 


28 


29 


27.25 


9.92 


27.21 


10.04 


27.16 


10.16 


27.12 


10.27 


29 


30 


28.19 


10.26 


28.15 


10.38 


28.10 


10.51 


23.05 


10.63 


30 


31 


29.13 


10.60 


29.08 


10.73 


29.04 


10.86 


28.99 


10.98 


31 


32 


30.07 


10.94 


30.02 


11.08 


29.97 


11.21 


29.92 


11.34 


32 


33 


31.01 


11.29 


30.96 


11.42 


30.91 


11.56 


30.86 


11.69 


33 


34 


31.95 


11.63 


31.90 


11.77 


31.85 


11.91 


31.79 


12.05 


34 


35 


32.89 


11.97 


32.84 


12.11 


32.78 


12.26 


32.73 


12.40 


35 


36 


33.83 


12.31 


33.77 


12.46 


33.72 


12.61 


33.66 


12.75 


36 


37 


34.77 


12.65 


34.71 


12.81 


34.66 


12.96 


34.60 


13.11 


37 


38 


35.71 


13.00 


35.65 


13.15 


35.59 


13.31 


35.54 


13.46 


38 


39 


36.65 


13.34 


36.59 


13.50 


36.53 


13.66 


36.47 


13.82 


39 


40 


37.59 


13.68 


37.53 


13.84 


37.47 


14.01 


37.41 


14.17 


40 


41 


38.53 


14.02 


38.47 


14.19 


38.40 


14.36 


38.34 


14.53 


41 


42 


39.47 


14.36 


39.40 


14.54 


39.34 


14.71 


39.28 


14.88 


42 


43 


40.41 


14.71 


40.34 


14.88 


40.28 


15.06 


40.21 


15.23 


43 


44 


41.35 


15.05 


41.28 


15.23 


41.21 


15.41 


41.15 


15.59 


44 


45 


42.29 


15.39 


42.22 


15.58 


42.15 


15.76 


42.08 


15.94 


45 


46 


43.23 


15.73 


43.16 


15.92 


43.09 


16.11 


43.02 


16.30 


46 


47 


44.17 


16.07 


44.09 


16.27 


44.02 


16.46 


43.95 


16.65 


47 


48 


45.11 


16.42 


45.03 


16.61 


44.96 


16.81 


44.89 


17.01 


48 


49 


46.04 


16.76 


45.97 


16.96 


45.90 


17.16 


45.82 


17.36 


49 


50 


46.98 


17.10 


46.91 


17.31 


46.83 


17.51 


46.76 | 


17.71 


50 


o 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 
69J 1 


Lat. 


£ 

a 

1:1 


70 1 


)eg. 


69| 


Deg. 


69* 


Deg. 


Deg. 1 



TRAVERSE TABLE. 



43 



g 

S3 
P 
O 
? 


20 Deg. 


204 Deg. 


20£ Deg. 


20| Deg. 


C 

D 
o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


47.92 


17.44 


47.85 


17.65 


47.77 


17.86 


47.69 


18.07 


51 


52 


48.86 


17.79 


48.79 


18.00 


48.71 


13.21 


48.63 


18.42 


52 


53 


49.80 


18.13 


49.72 


18.34 


49.64 


18.56 


49.56 


IS. 78 


53 


54 


50.74 


18.47 


50.66 


18.69 


50.58 


18.91 


50.50 


19.13 


54 


55 


51.68 


18.81 


51.60 


19.04 


51.52 


19.26 


51.43 


19.49 


55 


56 


52.62 


19.15 


52.54 


19.38 


52.45 


19.61 


52.37 


19.84 


56 \ 


57 


53.56 


19.50 


53.48 


19.73 


53.39 


19.96 


53.30 


20.19 


57 f 


58 


54.50 


19.84 


54.42 


20.07 


54.33 


20.31 


54.24 


20.55 


53 


39 


55.44 


20.18 


55.35 


20.42 


55.26 


20.66 


55.17 


20.90 


59 


60 


56.38 


20.52 


56.29 


20.77 


56.20 


21.01 


56.11 


21.26 


60 


61 


57.32 


20.86 


57.23 


21.11 


57.14 


21.36 


57.04 


21.61 


61 | 


62 


58.26 


21.21 


58.17 


21.46 


58.07 


21.71 


57.98 


21.97 


62 


63 


59.20 


21.55 


59.11 


21.81 


59.01 


22.06 


58.91 


22.32 


63 


64 


60.14 


21.89 


60.04 


22.15 


59.95 


22.41 


59.85 


22.67 


64 


65 


61.08 


22.23 


60.98 


22.50 


60.88 


22.76 


60.78 


23.03 


65 


66 


62.02 


22.57 


61.92 


22.84 


61.82 


23.11 


61.72 


23.38 


66 


67 


62.96 


22.92 


62.86 


23.19 


62.76 


23.46 


62.65 


23.74 


67 


68 


63.90 


23.26 


63.80 


23.54 


63.69 


23.81 


63.59 


24.09 


68 ; 


69 


64.84 


23.60 


64.74 


23.88 


64.63 


24.16 


64.52 


24.45 


69 


70 


65.78 


23.94 


65.67 


24.23 


65.57 


24.51 


65.46 


24.80 


70 


71 


66.72 


24.28 


66.61 


24.57 


66.50 


24.86 


66.39 


25.15 


71 


72 


67.66 


24.63 


67.55 


24.92 


67.44 


25.21 


67.33 


25.51 


72 


73 


68.60 


24.97 


68.49 


25.27 


68.38 


25.57 


68.26 


25.86 


73 


74 


69.54 


25.31 


69.43 


25.61 


69.31 


25.92 


| 69.20 


26.22 


74 


75 


70.48 


25.65 


70.36 


25.96 


70.25 


26.27 


70.14 


26.57 


75 


76 


71.42 


25.99 


71.30 


26.30 


71.19 


26.62 


71.07 


26.93 


76 


77 


72.36 


26.34 


72.24 


26.65 


72.12 


26.97 


72.01 


27.28 


77 


78 


73.30 


26.68 


73.18 


27.00 


73.06 


27.32 


72.94 


27.63 


78 


79 


74.24 


27.02 


74.12 


27.34 


74.00 


27.67 


73.88 


27.99 


79 


80 


75.18 


27.36 


75.06 


27.69 


74.93 


28.02 


74.81 


28.34 


80 


81 


76.12 


27.70 


75.99 


28.04 


75.87 


28.37 


75.75 


28.70 


81 


82 


77.05 


28.05 


76.93 


28.38 


76.81 


28.72 


76.68 


29.05 


82 


83 


77.99 


28.39 


77.87 


28.73 


77.74 


29.07 


77.62 


29.41 


83 


84 


78.93 


28.73 


78.81 


29.07 


78.68 


29.42 


78.55 


29.76 


84 


85 


79.87 


29.07 


79.75 


29.42 


79.62 


29.77 


79.49 


30.11 


35 


86 
87 


80.81 


29.41 


80.68 


29.77 


80.55 


30.12 


80.42 


30.47 


86 


81.75 


29.76 


81.62 


30.11 


81.49 


30.47 


81.36 


30.82 


87 


88 


82.69 


30.10 


82.56 


30.46 


82.43 


30.82 


82.29 


31.18 


88 


89 


83.63 


30.44 


83.50 


30.80 


83.36 


31.17 


83.23 


31.53 


39 


90 


84.57 


30.78 


84.44 


31.15 


84.30 


31.52 


84.16 


31.89 


90 


91 


85.51 


31.12 


85.38 


31.50 


85.24 


31.87 


85.10 


32.24 


91 


92 


86.45 


31.47 


86.31 


31.84 


86.17 


32.22 


86.03 


32.59 


92 


93 


87.39 


31.81 


87.25 


32.19 


87.11 


32.57 


86.97 


32.95 


93 


94 


88.33 


32.15 


88.19 


32.54 


88.05 


32.92 


87.90 


33.30 


94 


95 


89.27 


32.49 


89.13 


32.88 


88.98 


33.27 


88.84 


33.66 


95 


96 


90.21 


32.83 


90.07 


33.23 


89.92 


33.62 


89.77 


34.01 


96 


97 


91 . 15 


33.18 


91.00 


33.57 


90.86 


33.97 


90.71 


34.37 


97 


98 


92.09 


33.52 


91.94 


33.92 


91.79 


34.32 


91.64 


34.72 


98 


99 


93.03 


33.86 


92.88 


34.27 


92.73 


34.67 


92.58 


35.07 


99 


100 


93.97 


34.20 


93.82 


34.61 


93.67 


35.02 


93.51 


35.43 


100 


o 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


0) 
D 

a 


70 1 


)eg. • 
! 


69| 


Deg. 


69i Deg. 


694 Deg. 



44 



TRAVERSE TABLE. 





o 
? 


21 Deg. 


2H Deg. 


21 i Deg. 


21| Deg. 


o 

V 
3 
O 
? 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


0.93 


0.36 


0.93 


0.36 


0.93 


0.37 


0.93 


0.37 


1 




2 


1.87 


0.72 


1.86 


0.72 


1.86 


0.73 


1.86 


0.74 


2 




3 


2.80 


1.08 


2.80 


1.09 


2.79 


1.10 


2.79 


1.11 


3 




4 


3.73 


1.43 


3.73 


1.45 


3.72 


1.47 


3.72 


1.48 


4 




5 


4.67 


1.79 


4.66 


1.81 


4.65 


1.83 


4.64 


1.85 


5 




6 


5.60 


2.15 


5.59 


2.17 


5.58 


2.20 


5.57 


2.22 


6 




7 


6.54 


2.51 


6.52 


2.54 


6.51 


2.57 


6.50 


2.59 


7 




8 


7.47 


2.87 


7.46 


2.90 


7.44 


2.93 


7.43 


2.96 


8 




9 


8.40 


3.23 


8.39 


3.26 


8.37 


3.30 


8.36 


3.34 


9 




10 


9.34 


3.58 


9.32 


3.62 


9.30 


3.67 


9.29 


3.71 


10 




11 


10.27 


3.94 


10.25 


3.99 


10.23 


4.03 


10.22 


4.08 


11 




12 


11.20 


4.30 


11.18 


4.35 


11.17 


4.40 


11.15 


4 45 


12 




13 


12.14 


4.66 


12.12 


4.71 


12.10 


4.76 


12.07 


4.82 


13 




14 


13.07 


5.02 


13.05 


5.07 


13.03 


5.13 


13.00 


5.19 


14 




15 


14.00 


5.38 


13.98 


5.44 


13.96 


5.50 


13.93 


5.56 


15 




16 


14.94 


5.73 


14.91 


5.80 


14.89 


5.86 


14.86 


5.93 


16 




17 


15.87 


6.09 


15.84 


6.16 


15.82 


6.23 


15.79 


6.30 


17 




18 


16.80 


6.45 


16.78 


6.52 


16.75 


6.60 


16.72 


6.67 


18 




19 


17.74 


6.81 


17.71 


6.89 


17.68 


6.96 


17.65 


7.04 


19 




20 


13.67 


7.17 


18.64 


7.25 


18.61 


7.33 


18.58 


7.41 
7.78 


20 
21 




21 


19.61 


7.53 


19.57 


7.61 


19.54 


7.70 


19.50 




22 


20.54 


7.88 


20.50 


7.97 


20.47 


8.06 


20.43 


8.15 


22 




23 


21.47 


8.24 


21.44 


8.34 


21.40 


8.43 


21.36 


8.52 


23 




24 


22.41 


8.60 


22.37 


8.70 


22.33 


8.80 


22.29 


8.89 


24 




25 


23.34 


8.96 


23.30 


9-06 


23.26 


9.16 


23.22 


9.26 


25 




26 


24.27 


9.32 


24.23 


9.42 


24.19 


9.53 


24.15 


9.63 


26 




27 


25.21 


9.68 


25.16 


9.79 


25.12 


9.90 


25.08 


10.01 


27 




28 


26.14 


10.03 


26.10 


10.15 


26.05 


10.26 


26-01 


10.38 


28 




29 


27.07 


10.39 


27.03 


10.51 


26.98 


10.63 


26.94 


10.75 


29 




30 


28.01 


10.75 


27.96 


10.87 


27.91 


11.00 


27.86 


11.12 


30 




31 


28.94 


11.11 


28.89 


11.24 


28.84 


11.36 


28.79 


11.49 


31 




32 


29.87 


11.47 


29.82 


11.60 


29.77 


11.73 


29.72 


11.86 


32 




33 


30.81 


11.83 


30.76 


11.96 


30.70 


12.09 


30.65 


12.23 


33 




34 


31.74 


12.18 


31.69 


12.32 


31.63 


12.46 


31.58 


12.60 


34 




35 


32.68 


12.54 


32.62 


12.69 


32.56 


12.83 


32.51 


12.97 


35 




36 


33.61 


12.90 


33.55 


13.05 


33.50 


13.19 


33.44 


13.34 


36 




37 


34.54 


13.26 


34.48 


13.41 


34.43 


13.56 


34.37 


13.71 


37 




38 


35.48 


13.62 


35.42 


13.77 


35.36 


13.93 


35.29 


14.08 


38 




39 


36.41 


13.98 


36.35 


14.14 


36.29 


14.29 


36.22 


14.45 


39 




40 
41 


37.34 


14.33 


37.28 


14.50 


37.22 


14.66 


37.15 


14.82 


40 




38.28 


14.69 


38.21 


14.86 


38.15 


15.03 


38.08 


15.19 


41 




42 


39.21 


15.05 


39.14 


15.22 


39.08 


15.39 


39.01 


15.56 


42 




43 


40.14 


15.41 


40.08 


15.58 


40.01 


15.76 


39.94 


15.93 


43 




44 


41.08 


15.77 


41.01 


15.95 


40.94 


16.13 


40.87 


16.30 


44 




45 


42.01 


16.13 


41.94 


16.31 


41.87 


16.49 


41.80 


16.68 


45 




46 


42.94 


16.48 


42.87 


16.67 


42.80 


16.86 


42.73 


17.05 


46 




47 


43.88 


16.84 


43.80 


17.03 


43.73 


17.23 


43.65 


17 42 


47 




48 


44.81 


17.20 


44.74 


17.40 


44.66 


17.59 


44.58 


17.79 


48 




49 


45.75 


17.56 


45.67 


17.76 


45.59 


17.96 


45.51 


18.16 


49 




50 


46.68 


17.92 


46.60 


18.12 


46.52 


18.33 


46.44 


18.53 


50 




o 

3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


■ 
o 

c 

5 




69 1 


3eg. 


68} Deg. 


68i 


Deg. 


68* 


Deg. 



TRAVERSE TABLE. 



45 





o 

s 
o 
? 


21 Deg. 


21} Deg. 


21i 


Deg. 


21| Deg. 


O 
? 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




51 


47.61 


18.28 


47.53 


18.48 


47.45 


18.69 


47.37 


18.90 


51 




52 


48.55 


18.64 


48.46 


18.85 


48.38 


19.06 


48.30 


19.27 


52 




53 


49.48 


18.99 


49.40 


19.21 


49.31 


19.42 


49.23 


19.64 


53 




54 


50.41 


19.35 


50.33 


19.57 


50.24 


19.79 


50.16 


20.01 


54 




55 


51.35 


19.71 


51.26 


19.93 


51.17 


20.16 


51.08 


20.38 


55 




56 


52.28 


20.07 


52.19 


20.30 


52.10 


20.52 


52.01 


20.75 


5^ ' 


! 


57 


53.21 


20.43 


53.12 


20.66 


53.03 


20.89 


52.94 


21.12 


57 




58 


54.15 


20.79 


54.06 


21.02 


53.96 


21.26 


53.87 


21.49 


58 




59 


55.08 


21.14 


54.99 


21.38 


54.89 


21.62 


54.80 


21.86 


59 




60 


56.01 


21.50 


55.92 


21.75 


55.83 


21.99 


55.73 


22.23 


60 ' 




61 


56.95 


21.86 


56.85 


22.11 


56.76 


22.36 


56.66 


22.60 


61 


; 


62 


57.88 


22.22 


57.78 


22.47 


57.69 


22.72 


57.59 


22.97 


62 : 




63 


58.82 


22.58 


58.72 


22.83 


58.62 


23.09 


58.52 


23.35 


63 


; 


64 


59.75 


22.94 


59.65 


23.20 


59.55 


23.46 


59.44 


23.72 


64 


■ 


65 


60.68 


23.29 


60.58 


23.56 


60.48 


23.82 


60.37 


24.09 


65 




66 


61.62 


23.65 


61.51 


23.92 


61.41 


24.19 


61.30 


24.46 


66 '■ 




67 


62.55 


24.01 


62.44 


24.28 


62.34 


24.56 


62.23 


24.83 


67 


■ 


68 


63.48 


24.37 


63.38 


24.65 


63.27 


24.92 


63.16 


25.20 


68 




69 


64.42 


24.73 


64.31 


25.01 


64.20 


25.29 


64.09 


25.57 


69 




70 


65.35 


25.09 


65.24 


25.37 


65.13 


25.66 


65.02 


25.94 


70 




71 


66.28 


25.44 


66.17 


25.73 


66.06 


26.02 


65.95 


26.31 


71 




72 


67.22 


25.80 


67.10 


26.10 


66.99 


26.39 


66.87 


26.68 


72 




73 


68.15 


26.16 


68.04 


26.46 


67.92 


26.75 


67.80 


27.05 


73 


i 


74 


69.08 


26.52 


68 97 


26.82 


68.85 


27.12 


68.73 


27.42 


74 


: 


75 


70.02 


26.88 


69.90 


27.18 


69.78 


27.49 


69.66 


27.79 


75 


'. 


76 


70.95 


27.24 


70.83 


27.55 


70.71 


27.85 


70.59 


28.16 


76 ' 


77 


71.89 


27.59 


71.76 


27.91 


71.64 


28.22 


71.52 


28.53 


77 : 


' 


78 


72.82 


27.95 


72.70 


28.27 


72.57 


28.59 


72.45 


28.90 


78 : 




79 


73.75 


28.31 


73.63 


28.63 


73.50 


28.95 


73.38 


29.27 


79 




80 


74.69 


28.67 


74.56 


29.00 


74.43 


29.32 


74.30 


29.64 


80 




81 


75.62 


29.03 


75.49 


29.36 


75.36 


29.69 


75.23 


30.02 


8i : 




82 


76.55 


29.39 


76.42 


29.72 


76.29 


30.05 


76.16 


30.39 


82 


' 


83 


77.49 


29.74 


77.36 


30.08 


77.22 


30.42 


77.09 


30.76 


83 


| 


84 


78.42 


30.10 


78.29 


30.44 


78.16 


30.79 


78.02 


31.13 


84 




85 


79.35 


30.46 


79.22 


30.81 


79.09 


31.15 


78.95 


31.50 


85 




86 


80.29 


30.82 


80.15 


31.17 


80.02 


31.52 


79.88 


31.87 


86 




87 


81.22 


31.18 


81.08 


31.53 


80.95 


31.89 


80.81 


32.24 


87 




88 


82.16 


31.54 


82.02 


31.89 


81.88 


32.25 


81.74 


32.61 


88 




89 


83.09 


31.89 


82.95 


32.26 


82.81 


32.62 


82.66 


32.98 


89 




90 


84.02 


32.25 


83.88 


32.62 


83.74 


32.99 


83.59 


33.35 


90 




91 


84.96 


32.61 


84.81 


32.98 


84.67 


33.35 


84.52 


33.72 


91 




92 


85.89 


32.97 


85.74 


33.34 


85.60 


33.72 


85.45 


34.09 


92 ' 




93 


86.82 


33.33 


86.68 


33.71 


86.53 


34.08 


86.38 


34.46 


93 




94 


87.76 


33.69 


87.61 


34.07 


87.46 


34.45 


87.31 


34.83 


94 




95 


88.69 


34.04 


88.54 


34.43 


88.39 


34.82 


88.24 


35.20 


95 ' 




96 


89.62 


34.40 


89.47 


34.79 


89.32 


35.18 


89.17 


35.57 


96 


97 


90.56 


34.76 


90.40 


35.16 


90.25 


35.55 


90.09 


35.94 


97 




98 


91.49 


35.12 


91.34 


35.52 


91.18 


35.92 


91.02 


36.31 


98 




99 


92.42 


35.48 


92.27 


35.88 


92.11 


36.28 


91.95 


36.69 


99 




100 


93.36 


35.84 


93.20 


36.24 


93.04 


36.65 


92.88 


37.06 


100 




o 
I 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o3 
o 

5 




69 Deg. 


68| 


Deg. 


68i 


Deg. 


68} Deg. 



28 



TRAVERSE TABLE. 




TRAVERSE TABLE. 



o 

ST 

o 


22Deg. 


22i Deg. 


22i Deg. 


22| Deg. 


2 

a 

CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


47.29 


19.10 


47.20 


19.31 


47.12 


19.52 


47.03 


19.72 


51 


52 


48.21 


19.48 


48.13 


19.69 


48.04 


19.90 


47.95 


20.11 


52 


53 


49.14 


19.85 


49.05 


20.07 


48.97 


20.28 


48.88 


20.50 


53 


54 


50.07 


20.23 


49.98 


20.45 


49.89 


20.66 


49.80 


20.88 


54 


55 


51.00 


20.60 


50.90 


20.83 


50.81 


21.05 


50.72 


21.27 


55 


56 


51.92 


20.98 


51.83 


21.20 


51.74 


21.43 


51.64 


21.66 


56 


57 


52.85 


21.35 


52.76 


21.58 


52.66 


21.81 


52.57 


22.04 


57 


58 


53.78 


21.73 


53.68 


21.96 


53.59 


22.20 


53.49 


22.43 


58 


59 


54.70 


22.10 


54.61 


22.34 


54.51 


22.58 


54.41 


22.82 


59 f 


60 


55.63 


22.48 


55.53 


22.72 


55.43 


22.96 


55.33 


23.20 


60 


61 


56.56 


22.85 


56.47 


23.10 


56.36 


23.34 


56.25 


23.59 


61 


62 


57.49 


23.23 


57.38 


23.48 


57.28 


23.73 


57.18 


23.98 


62 ; 


63 


58.41 


23.60 


58.31 


23.85 


58.20 


24.11 


58.10 


24.36 


63 


64 


59.34 


23.97 


59.23 


24.23 


59.13 


24.49 


59.02 


24.75 


64 


65 


60.27 


24.35 


60.16 


24.61 


60.05 


24.87 


59.94 


25.14 


65 


66 


61.19 


24.72 


61.09 


24.99 


60.98 


25.26 


60.87 


25.52 


66 


67 


62.12 


25.10 


62.01 


25.37 


61.90 


25.64 


61.79 


25.91 


67 


68 


63.05 


25.47 


62.94 


25.75 


62.82 


26.02 


62.71 


26.30 


68 


69 


63.98 


25.85 


63.86 


26.13 


63.75 


26.41 


63.63 


26.68 


69 


70 


64.90 


26.22 


64.79 


26.51 


64.67 


26.79 


64.55 


27.07 


70 


71 


65.83 


26.60 


65.71 


26.88 


65.60 


27.17 


65.48 


27.46 


71 


72 


66.76 


26.97 


66.64 


27.26 


66.52 


27.55 


66.40 


27.84 


72 


73 


67.68 


27.35 


67.56 


27.64 


67.44 


27.94 


67.32 


28.23 


73 


74 


68.61 


27.72 


68.49 


28.02 


68-37 


28.32 


68.24 


28.62 


74 


75 


69 54 


28.10 


69.42 


28.40 


69.29 


28.70 


69.17 


29.00 


75 


76 


70.47 


28.47 


70.34 


28.78 


70.21 


29.08 


70.09 


29.39 


76 


77 


71.39 


28.84 


71.27 


29.16 


71.14 


29.47 


71.01 


29.78 


77 


78 


72.32 


29.22 


72.19 


29.53 


72.06 


29.85 


71.93 


30.16 


78 


79 


73.25 


29.59 


73.12 


29.91 


72.99 


30.23 


72.85 


30.55 


79 


80 


74.17 


29.97 


74.04 


30.29 


73.91 


30.61 


73.78 


30.94 


80 


81 


75.10 


30.34 


74.97 


30.67 


74.83 


31.00 


74.70 


31.32 


81 


82 


76.03 


30.72 


75.89 


31.05 


75.76 


31.38 


75.62 


31.71 


82 


83 


76.96 


31.09 


76.82 


31.43 


76.68 


31.76 


76.54 


32.10 


83 


84 


77.88 


31.47 


77.75 


31.81 


77.61 


32.15 


77.46 


32.48 


84 


85 


78.81 


31.84 


78.67 


32.19 


1 78.53 


32.53 


78.39 


32.87 


85 


86 


79.74 


32.22 


79.60 


32.56 


79.45 


32.91 


79.31 


33.26 


86 


87 


80.66 


32.59 


80.52 


32.94 


80.38 


33.29 


80.23 


33.64 


87 


88 


81.59 


32.97 


81.45 


33.32 


81.30 


33.68 


81.15 


34.03 


88 


89 


82.52 


33.34 


82.37 


33.70 


82.23 


34.06 


82.08 


34.42 


89 


90 


83.45 


33.71 


83.30 


34.08 


83.15 


34.44 


83.00 


34.80 


90 


91 


84.37 


34.09 


84.22 


34.46 


84.07 


34.82 


83.92 


35.19 


91 


92 


85.30 


34.46 


85.15 


34.84 


85.00 


35.21 


84.84 


35.58 


92 


93 


86.23 


34.84 


86.08 


35.21 


85.92 


35.59 


85.76 


35.96 


93 


94 


87.16 


35.21 


87.00 


35.59 


86.84 


35.97 


86.69 


36.35 


94 


95 


88.08 


35.59 


87.93 


35.97 


87.77 


36.35 


87.61 


36.74 


95 


96 


89.01 


35.96 


88.85 


36.35 


88.69 


36.74 


88.53 


37.12 


96 


97 


89.94 


36.34 


89.78 


36.73 


89.62 


37.12 


89.45 


37.51 


97 


98 


90.86 


36.71 


90.70 


37.11 


90.54 


37.50 


90.38 


37.90 


98 


99 


91.79 


37.09 


91.63 


37.49 


91.46 


37.89 


91.30 


38.28 


99 


100 


92.72 


37.46 


92.55 


37.86 


92.39 


38.27 


92.22 


38.67 


100 


Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


e 
Q 


68 Deg. 


67J 


Deg. 


67* 


Deg. 


67\ Deg. 



48 



TRAVERSE TABLE. 



o 

S? 
a 
o 
a 


23 Deg. 


23* Deg. 


23* Deg. 


23} Deg. 


i 

s 
S 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.92 


0.39 


0.92 


0.39 


0.92 


0.40 


0.92 


0.40 


1 


2 


1.84 


0.78 


1.84 


0.79 


1.83 


0.80 


1.83 


0.81 


y 


3 


2.76 


1.17 


2.76 


1.18 


2.75 


1.20 


2.75 


: .21 


3 


4 


3.68 


1.56 


3.68 


1.58 


3.67 


1.59 


3.66 


'..61 


4 


5 


4.60 


1.95 


4.59 


1.97 


4.59 


1.99 


4.58 


2.01 


5 


6 


5.52 


2.34 


5.51 


2.37 


5.50 


2.39 


5.49 


2.42 


6 


7 


6.44 


2.74 


6.43 


2.76 


6.42 


i.79 


6.41 


2.82 


7 


8 


7.36 


3.13 


7.35 


3.16 


7.34 


3.19 


7.32 


3.22 


8 t 


9 


8.28 


3.52 


8.27 


3.55 


8.25 


3.59 


8.24 


3.62 


9 


10 


9.20 


3.91 


9.19 


3.95 


9.17 


3.99 


9.15 


4.03 


10 


11 


10.13 


4.30 


10.11 


4.34 


10.09 


4.39 


10.07 


4.43 


11 


12 


11.05 


4.69 


11.03 


4.74 


11.00 


4.78 


10.98 


4.83 


12 


13 


11.97 


5.08 


11.94 


5.13 


11.92 


5.18 


11.90 


5.24 


13 


14 


12.89 


5.47 


12.86 


5.53 


12.84 


5.58 


12.81 


5.64 


14 


15 


13.81 


5.86 


13.78 


5.92 


13.76 


5.98 


13.73 


6.04 


15 


16 


14.73 


6.25 


14.70 


6.32 


14.67 


6.38 


14.64 


6.44 


16 


17 


15.65 


6.64 


15.62 


6.71 


15.59 


6.78 


15.56 


6.85 


17 


18 


16.57 


7.03 


16.54 


7.11 


16.51 


7.18 


16.48 


7.25 


18 


19 


17.49 


7.42 


17.46 


7.50 


17.42 


7.58 


17.39 


7.65 


19 


20 


18.41 


7.81 


18.38 


7.89 


18.34 


7.97 


18.31 


8.05 


20 


21 


19.33 


8.21 


19.29 


8.29 


19.26 


8.37 


19.22 


8.46 


21 


22 


20.25 


8.60 


20.21 


8.68 


20.18 


8.77 


20.14 


8.86 


22 


. 23 


21.17 


8.99 


21.13 


9.08 


21.09 


9.17 


21.05 


9.26 


23 


24 


22.09 


9.38 


22.05 


9.47 


22.01 


9.57 


21.97 


9.67 


24 


25 


23.01 


9.77 


22.97 


9.87 


22.93 


9.97 


22.88 


10.07 


26 


26 


23.93 


10.16 


23.89 


10.26 


23.84 


10.37 


23.80 


10.47 


26 


27 


24.85 


10.55 


24.81 


10.66 


24.76 


10.77 


24.71 


10.87 


27 


28 


25.77 


10.94 


25.73 


11.05 


25.68 


11.16 


25.63 


11.28 


28 


29 


26.69 


11.33 


26.64 


11.45 


26.59 


11.56 


26.54 


11.68 


29 


30 


27.62 


11.72 


27.56 


11.84 


27.51 


11.96 


27.46 


12.08 


30 


31 


28.54 


12.11 


28.48 


12.24 


28.43 


12.36 


28.37 


12.49 


31 


32 


29.46 


12.50 


29.40 


12.63 


29.35 


12.76 


29.29 


12.89 


32 


33 


30.38 


12.89 


30.32 


13.03 


30.26 


13.16 


30.21 


13.29 


33 


34 


31.30 


13.28 


31.24 


13.42 


31.18 


13.56 


31.12 


13.69 


34 


35 


32.22 


13.68 


32.16 


13.82 


32.10 


13.96 


32.04 


14.10 


35 


36 


33.14 


14.07 


33.08 


14.21 


33.01 


14.35 


32.95 


14.50 36 


37 


34.06 


14.46 


34.00 


14.61 


33.93 


14.75 


33.87 


14.90 


37 


33 


34.98 


14.85 


34.91 


15.00 


34.85 


15.15 


34.78 


15.30 


38 


39 


35.90 


15.24 


35.83 


15.39 


35.77 


15.55 


35.70 


15.71 


39 


40 


36.82 


15.63 


36.75 


15.79 


36.68 


15.95 


36.61 


16.11 


40 


41 


37.74 


16.02 


37.67 


16.18 


37.60 


16.35 


37.53 


16.51 


41 


42 


38.66 


16.41 


38.59 


16.58 


38.52 


16.75 


38.44 


16.92 


42 


43 


39.58 


16.80 


39.51 


16.97 


39.43 


17.15 


39.36 


17.32 


43 


44 


40.50 


17.19 


40.43 


17.37 


40.35 


17.54 


40.27 


17.72 


44 


45 


41.42 


17.58 


41.35 


17.76 


41.27 


17.94 


41.19 


18.12 


45 


46 


42.34 


17.97 


42.26 


18.16 


42.18 


18.34 


42.10 


18.53 


46 


47 


43.26 


18.36 


43.18 


18.55 


43.10 


18.74 


43.02 


18.93 


47 


48 


44.18 


18.76 


44.10 


18-95 


44.02 


19.14 


43.93 


19.33 


48 


49 


45.10 


19.15 


45.02 


19.34 


44.94 


19.54 


44.85 


19.73 


49 


50 


46.03 


19.54 


45.94 


19.74 


45.85 


19.94 


45.77 


20.14 


50 


u 

6 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


M 


67 I 


)eg. 


66} 


Deg. 


66* Deg. 


66}] 


Deg. 


' 



TRAVERSE TABLE. 



49 



g 

1 


23 Deg. 


m Deg. 


23h Deg. 


23| Deg. 


g | 

1 ' 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


46.95 


19.93 


46.86 


20.13 


46.77 


20.34 


46.68 


20.54 


51 


52 


47.87 


20.32 


47.78 


20.53 


47.69 


20.73 


47.60 


20.94 


52 


53 


48.79 


20.71 


48.70 


20.92 


48.60 


21.13 


48.51 


21.35 


53 


54 


49.71 


21.10 


49.61 


21.32 


49.52 


21.53 


49.43 


21.75 


54 


55 


50.63 


21.49 


50.53 


21.71 


50.44 


21.93 


50.34 


22.15 


55 


56 


51.55 


21.88 


51.45 


22.11 


51.36 


22.33 


51.26 


22.55 


56 


57 


52.47 


22.27 


52.37 


22.50 


52.27 


22.73 


52.17 


22.96 


57 


58 


53.39 


22.66 


53.29 


22.90 


53.19 


23.13 


53.09 


23.36 


58 


59 


54.31 


23.05 


54.21 


23.29 


54.11 


23.53 


54.00 


23.76 


59 


60 


55.23 


23.44 


55.13 


23.68 


55.02 


23.92 


54.92 


24.16 


60 


61 


56.15 


23.83 


56.05 


24.08 


55.94 


24.32 


55.83 


24.57 


61 


62 


57.07 


24.23 


56.97 


24.47 


56.86 


24.72 


56.75 


24.97 


62 


63 


57.99 


24.62 


57.88 


24.87 


57.77 


25.12 


57.66 


25.37 


63 


64 


58.91 


25.01 


58.80 


25.26 


58.69 


25.52 


58.58 


25.78 


64 


65 


59.83 


25.40 


59.72 


25.66 


59.61 


25.92 


59.50 


26.18 


65 


66 


60.75 


25.79 


60.64 


26.05 


60.53 


26.32 


60.41 


26.58 


66 


67 


61.67 


26.18 


61.56 


26.45 


61.44 


26.72 


61.33 


26.98 


67 


68 


62.59 


26.57 


62.48 


26.84 


62.36 


27.11 


62.24 


27.39 


68 


69 


63.51 


26.96 


63.40 


27.24 


63.28 


27.51 


63.16 


27.79 


69 ' 


70 


64.44 


27.35 


64.32 


27.63 


64.19 


27.91 


64.07 


28.19 


70 


71 


65.36 


27.74 


65.23 


28.03 


65.11 


28.31 


64.99 


28.59 


71 


72 


66.28 


28.13 


66.15 


28.42 


66.03 


28.71 


65.90 


29.00 


72 


73 


67.20 


28.52 


67.07 


28.82 


66.95 


29.11 


66.82 


29.40 


73 


74 


68.12 


28.91 


67.99 


29.21 


67.86 


29.51 


67.73 


29.80 


74 


75 


69.04 


29.30 


68.91 


29.61 


68.78 


29.91 


68.65 


30.21 


75 


76 


69.96 


29.70 


69.83 


30.00 


69.70 


30.30 


69.56 


30.61 


76 


77 


70.88 


30.09 


70.75 


30.40 


70.61 


30.70 


70.48 


31.01 


77 


78 


71.80 


30.48 


71.67 


30.79 


71.53 


31.10 


71.39 


31.41 


78 ' 


79 


72.72 


30.87 


72.58 


31.18 


72.45 


31.50 


72.31 


31.82 


79 


80 


73.64 


31.26 


73.50 


31.58 


73.36 


31.90 


73.22 


32.22 


80 


81 


74.56 


31.65 


74.42 


31.97 


74.28 


32.30 


74.14 


32.62 


81 


82 


75.48 


32.04 


75.34 


32.37 


75.20 


32.70 


75.06 


33.03 


82 


83 


76.40 


32.43 


76.26 


32.76 


76.12 


33.10 


75.97 


33.43 


83 


84 


77.32 


32.82 


77.18 


33.16 


77.03 


33.49 


76.89 


33.83 


84 


85 


78.24 


33.21 


78.10 


33.55 


77.95 


33.89 


77.80 


34.23 


85 


86 


79.16 


33.60 


79.02 


33.95 


78.87 


34.29 


78.72 


34.64 


86 


87 


80.08 


33.99 


79.93 


34.34 


79.78 


34.69 


79.63 


35.04 


87 


88 


81.00 


34.38 


80.85 


34.74 


80.70 


35.09 


80.55 


35.44 


88 


89 


81.92 


34.78 


81.77 


35.13 


81.62 


35.49 


81.46 


35.84 


89 


90 


82.85 


35.17 


82.69 


35.53 


82.54 


35.89 


82.38 


36.25 


90 


91 


83.77 


35.56 


83.61 


35.92 


83.45 


36.29 


83.29 


36.65 


91 


92 


84.69 


35.95 


84.53 


36.32 


84.37 


36.68 


84.21 


37.05 


92 


93 


85.61 


36.34 


85.45 


36.71 


85.29 


37.08 


85.12 


37.46 


93 


94 


86.53 


36.73 


86.37 


37.11 


86.20 


37.48 


86.04 


37.86 


94 


95 


87.45 


37.12 


87.29 


37.50 


87 12 


37.88 


86.95 


38.26 


95 


96 


88.37 


37.51 


88.20 


37.90 


88.04 


38.28 


87.87 


38.66 


96 


97 


89.29 


37.90 


89.12 


38.29 


88.95 


38.68 


88.79 


39.07 


97 


98 


90.21 


38.29 


90.04 


38.68 


89.87 


39.08 


89.70 


39.47 


98 


99 


91.13 


38.68 


90.96 


39.08 


90.79 


39.48 


90.62 


39.87 


99 


100 


92.05 


39.07 


91.88 


39.47 


91.71 


39.87 


91.53 


40.27 


100 


o 

S3 

3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


0) 

o 

a 

Q 


67 


Deg. 


66f 


Deg. 


66^ Deg. 


66i Deg. 



2T 



50 



TRAVERSE TABLE. 



1 

o 
? 


24 Deg. 


24i Deg. 


24i Deg. 


241 Deg. 


q 

ST 

B 
O 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.91 


0.41 


0.91 


0.41 


0.91 


0.41 


0.91 


0.42 


1 


2 


1.83 


0.81 


1.82 


0.82 


1.82 


0.83 


1.82 


0.84 


2 


3 


2.74 


1.22 


2.74 


1.23 


2.73 


1.24 


2.72 


1.26 


3 


4 


3.65 


1.63 


3.65 


1.64 


3.64 


1.66 


3.63 


1.67 


4 


5 


4.57 


2.03 


4.56 


2.05 


4.55 


2.07 


4.54 


2.09 


5 


6 


5.48 


2.44 


5.47 


2.46 


5.46 


2.49 


5.45 


2.51 


6 


7 


6.39 


2.85 


6.38 


2.87 


6.37 


2.90 


6.36 


2.93 


7 


8 


7.31 


3.25 


7.29 


3.29 


7.28 


3.32 


7.27 


3.35 


8 


9 


8.22 


3.66 


8.21 


3.70 


8.19 


3.73 


8.17 


3.77 


9 


10 


9.14 


4.07 


9.12 


4.11 


9.10 


4.15 


9.03 


4.19 


10 . 


11 


10.05 


4.47 


10.03 


4.52 


10.01 


4.56 


9.99 


4.61 


11 


12 


10.96 


4.88 


10.94 


4.93 


10.92 


4.98 


10.90 


5.02 


12 


13 


11.88 


5.29 


11.85 


5.34 


11.83 


5.39 


11.81 


5.44 


13 


14 


12.79 


5.69 


12.76 


5.75 


12.74 


5.81 


12.71 


5.86 


14 


15 


13.70 


6.10 


13.68 


6.16 


13.65 


6.22 


13.62 


6.28 


15 


16 


14.62 


6.51 


14.59 


6.57 


14.56 


6.64 


14.53 


6.70 


16 


17 


15.53 


6.92 


15.50 


6.93 


15.47 


7.05 


15.44 


7.12 


17 


18 


16.44 


7.32 


16.41 


7.39 


16.38 


7.46 


16.35 


7.54 


18 1 


19 


17.36 


7.73 


17.32 


7.80 


17.29 


7.88 


17.25 


7.95 


19 


20 


18.27 


8.13 


18.24 


8.21 


18.20 


8.29 


18.16 


8.37 


20 


21 


19.18 


8.54 


19.15 


8.63 


19.11 


8.71 


19.07 


8.79 


21 


22 


20.10 


8.95 


20.06 


9.04 


20.02 


9.12 


19.98 


9.21 


22 


23 


21.01 


9.35 


20.97 


9.45 


20.93 


9.54 


20.89 


9.63 


23 


24 


21.93 


9.76 


21.88 


9.86 


21.84 


9.95 


21.80 


10.05 


24 


25 


22.84 


10.17 


22.79 


10.27 


22.75 


10.37 


22.70 


10.47 


25 


26 


23.75 


10.58 


23.71 


10.68 


23.66 


10.78 


23.61 


10.89 


26 


27 


24.67 


10.98 


24.62 


11.09 


24.57 


11.20 


24.52 


11.30 


27 


28 


25.58 


11.39 


25.53 


11.50 


25.48 


11.61 


25.43 


11.72 


28 


29 


26.49 


11.80 


26.44 


11.91 


26.39 


12.03 


26.34 


12.14 


29 


30 


27.41 


12.20 


27.35 


12.32 


27.30 


12.44 


27.24 


12.56 


30 


31 


28.32 


12.61 


28.26 


12.73 


28.21 


12.86 


28.15 


12.98 


31 


32 


29.23 


13.02 


29.18 


13.14 


29.12 


13.27 


29.06 


13.40 


32 


33 


30.15 


13.42 


30.09 


13.55 


30.03 


13.68 


29.97 


13.82 


33 


34 


31.06 


13.83 


31.00 


13.96 


30.94 


14.10 


30.88 


14.23 


34 


35 


31.97 


14.24 


31.91 


14.38 


31.85 


14.51 


31.78 


14.65 


35 


36 


32.89 


14.64 


32.82 


14.79 


32.76 


14.93 


32.69 


15.07 


36 


37 


33.80 


15.05 


33.74 


15.20 


33.67 


15.34 


33.60 


15.49 


37 


38 


34.71 


15.46 


34.65 


15.61 


34.58 


15.76 


34.51 


15.91 


38 


39 


35.63 


15.86 


35.56 


16.02 


35.49 


16.17 


35.42 


16.33 


39 


40 


36.54 


16.27 


36.47 


16.43 


36.40 


16.59 


36.33 


16.75 


40 


41 


37.46 


16.63 


37.38 


16.84 


37.31 


17.00 


37.23 


17.16 


41 


42 


38.37 


17.03 


38.29 


17.25 


38.22 


17.42 


38.14 


17.58 


42 


43 


39.28 


17.49 


39.21 


17.66 


39.13 


17.83 


39.05 


13.00 


43 


44 


40.20 


17.90 


40.12 


18.07 


40.04 


18.25 


39.96 


18.42 


44 


45 


41.11 


18.30 


41.03 


18.48 


40.95 


18.66 


40.87 


18.84 


45 


46 


42.02 


18.71 


41.94 


18.89 


41.86 


19.08 


41.77 


19.26 


46 


47 


42.94 


19.12 


42.85 


19.30 


42.77 


19.49 


42.68 


19.63 


47 


43 


43.85 


19.52 


43.76 


19.71 


43.63 


19.91 


43.59 


20.10 


48 


49 


44.76 


19.93 


44.68 


20.13 


44.59 


20.32 


44.50 


20.51 


49 


50 


45.68 


20.34 


45.59 


20.54 


45.50 


20.73 


45.41 


20.93 


50 ; 


a 

S3 

3 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


<u 1 

- f 

si I 

a| 


66 1 


)eg. 


65f Deg. 


65* 


Deg. 


65i 


Deg. 



TRAVERSE TABLE. 



51 





p 
a 
o 

(0 


24 Deg. 


24} Deg. 


24* Deg. 


24| Deg. 


O 
S" 

O 
(0 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




51 


46.59 


20.74 


46.50 


20.95 


46.41 


21.15 


46.32 


21.35 


51 




52 


47.50 


21.15 


47.41 


21.36 


47.32 


21.56 


47.22 


21.77 


52 




53 


48.42 


21.56 


48.32 


21.77 


48.23 


21.98 


48.13 


22.19 


53 




54 


49.33 


21.96 


49.24 


22.18 


49.14 


22.39 


49.04 


22.61 


54 




55 


50.24 


22.37 


50.15 


22.59 


50.05 


22.81 


49.95 


23.03 


55 




56 


51.16 


22.78 


51.06 


23.00 


50.96 


23.22 


50.86 


23.44 


56 




57 


52.07 


23.18 


51.97 


23.41 


51.87 


23.64 


51.76 


23.86 


57 




58 


52.99 


23.59 


52.88 


23.82 


52.78 


24.05 


52.67 


24.28 


58 




59 


53.90 


24.00 


53.79 


24.23 


53.69 


24.47 


53.58 


24.70 


59 


;■ 


60 


54.81 


24.40 


54.71 


24.64 


54.60 


24.88 


54.49 


25.12 


60 




61 


55.73 


24.81 


55.62 


25.05 


55.51 


25.30 


55.40 


25.54 


61 




62 


56.64 


25.22 


56.53 


25.46 


56.42 


25.71 


56.30 


25.96 


62 




63 


57.55 


25.62 


57.44 


25.88 


57.33 


26.13 


57.21 


26.38 


63 




64 


58.47 


26.03 


58.35 


26.29 


58.24 


26.54 


58.12 


26.79 


64 




65 


59.38 


26.44 


59.26 


26.70 


59.15 


26.96 


59.03 


27.21 


65 




66 


60.29 


26.84 


60.18 


27.11 


60.06 


27.37 


59.94 


27.63 


66 




67 


61.21 


27.25 


61.09 


27.52 


60.97 


27.78 


60.85 


28.05 


67 




68 


62.12 


27.66 


62.00 


27.93 


61.88 


28.20 


61.75 


28.47 


68 




69 


63.03 


28.06 


62.91 


28.34 


62.79 


28.61 


62.66 


28.89 


69 




70 


63.95 


28.47 


63.82 


28.75 


63.70 


29.03 


63.57 


29.31 


70 




71 


64.86 


28.88 


64.74 


29.16 


64.61 


29.44 


64.48 


29.72 


71 




: 72 


65.78 


29.28 


65.65 


29.57 


65.52 


29.86 


65.39 


30.14 


72 




73 


66.69 


29.69 


66.56 


29.98 


66.43 


30.27 


66.29 


30.56 


73 




74 


67.60 


30.10 


67.47 


30.39 


67.34 


30.69 


67.20 


30.98 


74 




75 


68.52 


30.51 


68.38 


30.80 


68.25 


31.10 


68.11 


31.40 


75 




76 


69.43 


30.91 


69.29 


31.21 


69.16 


31.52 


69.02 


31.82 


76 




77 


70.34 


31.32 


70.21 


31.63 


70.07 


31.93 


69.93 


32.24 


77 




78 


71.26 


31.73 


71.12 


32.04 


70.98 


32.35 


70.84 


32.66 


78 




79 


72.17 


32.13 


72.03 


32.45 


71.89 


32.76 


71.74 


33.07 


79 




80 


73.08 


32.54 


72.94 


32.86 


72.80 


33.18 


72.65 


33.49 


80 




81 


74.00 


32.95 


73.85 


33.27 


73.71 


33.59 


73.56 


33.91 


81 




82 


74.91 


33.35 


74.76 


33.68 


74.62 


34.00 


74.47 


34.33 


82 




83 


75.82 


33.76 


75.68 


34.09 


75.53 


34.42 


75.38 


34.75 


83 




84 


76.74 


34.17 


76.59 


34.50 


76.44 


34.83 


76.28 


35.17 


84 




85 


77.65 


34.57 


77.50 


34.91 


77.35 


35.25 


77.19 


35.59 


85 




86 


78.56 


34.98 


78.41 


35.32 


78.26 


35.66 


78.10 


36.00 


86 




87 


79.48 


35.39 


79.32 


35.73 


79.17 


36.08 


79.01 


36.42 


87 




88 


80.39 


35.79 


80.24 


36.14 


80.08 


36.49 


79.92 


36.84 


88 




89 


81.31 


36.20 


81.15 


36.55 


80.99 


36.91 


80.82 


37.26 


89 




90 


82.22 


36.61 


82.06 


36.96 


81.90 


37.32 


81.73 


37.68 


90 




91 


83.13 


37.01 


82.97 


37.38 


82.81 


37.74 


82.64 


38.10 


91 




92 


84.05 


37.42 


83.88 


37.79 


83.72 


38.15 


83.55 


38.52 


92 




93 


84.96 


37.83 


84.79 


38.20 


84.63 


38.57 


84.46 


38.94 


93 




94 


85.87 


38.23 


85.71 


38.61 


85.54 


38.98 


85.37 


39.35 


94 




95 


86.79 


38.64 


86.62 


39.02 


86.45 


39.40 


86.27 


39.77 


95 




96 


87.70 


39.05 


87.53 


39.43 


87.36 


39.81 


87.18 


40.19 


96 




97 


88.61 


39.45 


88.44 


39.84 


88.27 


40.23 


88.09 


40.61 


97 




98 


89.53 


39.86 


89.35 


40.25 


89.18 


40.64 


89.00 


41.03 


98 




99 


90.44 


40.27 


90.26 


40.66 


90.09 


41.05 


89.91 


41.45 


99 




100 


91.35 


40.67 


91.18 


41.07 


91.00 


41.47 


90.81 


41.87 


100 




6 

1 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 
o 

a 
3 

s 




66 Deg. 


65| Deg. 


65£ Deg. 


65}] 


Deg. 





52 



TRAVERSE TABLE. 



g 

p 

3 

a 
9 


25 


Deg. 


25i Deg. 


25} 


Deg. 


25} 


Deg. 


B 

i 
P 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.91 


0.42 


0.90 


0.43 


0.90 


0.43 


0.90 


0.43 


1 


2 


1.81 


0.85 


1.81 


0.85 


1.81 


0.86 


1.80 


0.87 


2 


3 


2.72 


1.27 


2.71 


1.28 


2.71 


1.29 


2.70 


1.30 


3 


4 


3.63 


1.69 


3.62 


1.71 


3.61 


1.72 


3.60 


1.74 


4 


5 


4.53 


2.11 


4.52 


2.13 


4.51 


2.15 


4.50 


2.17 


5 


6 


5.44 


2.54 


5.43 


2.56 


5.42 


2.58 


5.40 


2.61 


6 


7 


6.34 


2.96 


6.33 


2.99 


6.32 


3.01 


6.30 


3.04 


7 


3 


7.25 


3.38 


7.24 


3.41 


7.22 


3.44 


7.21 


3.48 


8 


9 


8.16 


3.80 


8.14 


3.84 


8.12 


3.87 


8.11 


3.91 


9 


10 


9.06 


4.23 


9.04 


4.27 


9.03 


4.31 


9.01 


4.34 


10 


11 


9.97 


4.65 


9.95 


4.69 


9.93 


4.74 


9.91 


4.78 


11 


12 


10.88 


5.07 


10.85 


5.12 


10.83 


5.17 


10.81 


5.21 


12 


13 


11.78 


5.49 


11.76 


5.55 


11.73 


5.60 


11.71 


5.65 


13 


14 


12.69 


5.92 


12.66 


5.97 


12.64 


6.03 


12.61 


6.08 


14 


15 


13.59 


6.34 


13.57 


6.40 


13.54 


6.46 


13.51 


6.52 


15 


16 


14.50 


6.76 


14.47 


6.83 


14.44 


6.89 


14.41 


6.95 


16 


17 


15.41 


7.18 


15.38 


7.25 


15.34 


7.32 


15.31 


7.39 


17 


18 


16.31 


7.61 


16.28 


7.68 


16.25 


7.75 


16.21 


7.82 


18 


19 


17.22 


8.03 


17.18 


8.10 


17.15 


8.18 


17.11 


8.25 


19 


20 


18.13 


8.45 


18.09 


8.53 


18.05 


8.61 


18.01 


8.69 


20 


21 


19.03 


8.87 


18.99 


8.96 


18.95 


9.04 


18.91 


9.12 


21 


22 


19.94 


9.30 


19.90 


9.38 


19.86 


9.47 


19.82 


9.56 


22 


23 


20.85 


9.72 


20.80 


9.81 


20.76 


9.90 


20.72 


9.99 


23 


24 


21.75 


10.14 


21.71 


10.24 


21.66 


10.33 


21.62 


10.43 


24 


25 


22.66 


10.57 


22.61 


10.66 


22.56 


10.76 


22.52 


10.86 


25 


26 


23.56 


10.99 


23.52 


11.09 


23.47 


11.19 


23.42 


11.30 


26 


27 


24.47 


11.41 


24.42 


11.52 


24.37 


11.62 


24.32 


11.73 


27 


28 


25.38 


11.83 


25.32 


11.94 


25.27 


12.05 


25.22 


12.16 


28 


29 


26.28 


12.26 


26.23 


12.37 


26.17 


12.48 


26.12 


12.60 


29 


, 30 


27.19 


12.68 


27.13 


12.80 


27.08 


12.92 


27.02 


13.03 


30 


31 


28.10 


13.10 


28.04 


13.22 


27.98 


13.35 


27.92 


13.47 


31 


32 


29.00 


13.52 


28.94 


13.65 


28.88 


13.78 


28.82 


13.90 


32 


33 


29.91 


13.95 


29.85 


14.08 


29.79 


14.21 


29.72 


14.34 


33 


34 


30.81 


14.37 


30.75 


14.50 


30.69 


14.64 


30.62 


14.77 


34 


35 


31.72 


14.79 


31.66 


14.93 


31.59 


15.07 


31.52 


15.21 


35 


36 


32.63 


15.21 


32.56 


15.36 


32.49 


15.50 


32.43 


15.64 


36 


37 


33.53 


15.64 


33.46 


15.78 


33.40 


15.93 


33.33 


16.07 


37 


38 


34.44 


16.06 


34.37 


16.21 


34.30 


16.36 


34.23 


16.51 


38 


39 


35.35 


16.48 


35.27 


16.64 


35.20 


16.79 


35.13 


16.94 


39 


40 


36.25 


16.90 


36.18 


17.06 


36.10 


17.22 


36.03 


17.38 


40 


41 


37.16 


17.33 


37.08 


17.49 


37.01 


17.65 


36.93 


17.81 


41 


42 


38.06 


17.75 


37.99 


17.92 


37.91 


18.08 


37.83 


18.25 


42 


43 


38.97 


18.17 


38.89 


18.34 


38-81 


18.51 


38.73 


18.68 


43 


44 


39.88 


18.60 


39.80 


18.77 


39.71 


18.94 


39.63 


19.12 


44 


45 


40.78 


19.02 


40.70 


19.20 


40.62 


19.37 


40.53 


19.55 


45 


46 


41.69 


19.44 


41.60 


19.62 


41.52 


19.80 


41.43 


19.98 


46 


47 


42.60 


19.86 


42.51 


20.05 


42.42 


20.23 


42.33 


20.42 


47 


48 


43.50 


20.29 


43.41 


20.43 


43.32 


20.66 


43.23 


20.85 


48 


49 


44.41 


20.71 


44.32 


20.90 


44.23 


21.10 


44.13 


21.29 


49 


50 


45.32 


21.13 


45.22 


21.33 


45.13 


21.53 


45.03 


21.72 


50 


a 

a 

! S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 

K 
5 


65 I 


)eg. 


64| 


Deg. 


64 i 


Deg. 


64} 


Deg. 



TRAVERSE TABLE. 



53 



1 


25 Deg. 


25i Deg. 


25i Deg. 


25| Deg. 


1 



3 

a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


46.22 


21.55 


46.13 


21.75 


46.03 


21.96 


45.94 


22.16 


51 


52 


47.13 


21.98 


47.03 


22.18 


46.93 


22.39 


46.84 


22.59 


52 


53 


48.03 


22.40 


47.94 


22.61 


47.84 


22.82 


47.74 


23.03 


53 


54 


48.94 


22.82 


48.84 


23.03 


48.74 


23.25 


48.64 


23.46 


54 


55 


49.85 


23.24 


49.74 


23.46 


49.64 


23.68 


49.54 


23.89 


55 


56 


50.75 


23.67 


50.65 


23.89 


50.54 


24.11 


50.44 


24.33 


56 


57 


51.66 


24.09 


51.55 


24.31 


51.45 


24.54 


51.34 


24.76 


57 ' 


' 58 


52.57 


24.51 


52.46 


24.74 


52.35 


24.97 


52.24 


25.20 


58 


59 


53.47 


24.93 


53.36 


25.17 


53.25 


25.40 


53.14 


25.63 


59 


60 


54.38 


25.36 


54.27 


25.59 


54.16 


25.83 


54.04 


26.07 


60 


61 


55.28 


25.78 


55.17 


26.02 


55.06 


26.26 


54.94 


26.50 


61 


' 62 


56.19 


26.20 


56.08 


26.45 


55.96 


26.69 


55.84 


26.94 


62 


, 63 


57.10 


26.62 


56.98 


26.87 


56.86 


27.12 


56.74 


27.37 


63 


64 


58.00 


27.05 


57.89 


27.30 


57.77 


27.55 


57.64 


27.80 


64 


65 


58.91 


27.47 


58.79 


27.73 


58.67 


27.98 


58.55 


28.24 


65 


66 


59.82 


27.89 


59.69 


28.15 


59.57 


28.41 


59.45 


28.67 


66 


67 


60.72 


28.32 


60.60 


28.58 


60.47 


28.84 


60.35 


29.11 


67 ' 


68 


61.63 


28.74 


61.50 


29.01 


61.38 


29.27 


61.25 


29.54 


68 


69 


62.54 


29.16 


62.41 


29.43 


62.28 


29.71 


62.15 


29.98 


69 


1 70 


63.44 


29.58 


63.31 


29.86 


63.18 


30.14 


63.05 


30.41 


70 


1 71 


64.35 


30.01 


64.22 


30.29 


64.08 


30.57 


63.95 


30.85 


71 , 


72 


65.25 


30.43 


65.12 


30.71 


64.99 


31.00 


64.85 


31.28 


72 


I 73 


66.16 


30.85 


66.03 


31.14 


65.89 


31.43 


65.75 


31.71 


73 


i 7 4 


67.07 


31.27 


66.93 


31.57 


66.79 


31.86 


66.65 


32.15 


74 


75 


67.97 


31.70 


67.83 


31.99 


67.69 


32.29 


67.55 


32.58 


75 


! 76 


68.88 


32.12 


68.74 


32.42 


68.60 


32.72 


68.45 


33.02 


76 


1 77 


69.79 


32.54 


69.64 


32.85 


69.50 


33.15 


69.35 


33.45 


77 : 


78 


70.69 


32.96 


70.55 


33.27 


70.40 


33.58 


70.25 


33.89 


78 


79 


71.60 


33.39 


71.45 


33.70 


71.30 


34.01 


71.16 


34.32 


79 ; 


80 


72.50 


33.81 


72.36 


34.13 


72.21 


34.44 


72.06 


34.76 


80 


81 


73.41 


34.23 


73.26 


34.55 


73.11 


34.87 


72.96 


35.19 


81 


82 


74.32 


34.65 


74.17 


34.98 


74.01 


35.30 


73.86 


35.62 


82 


83 


75.22 


35.08 


75.07 


35.41 


74.91 


35.73 


74.76 


36.06 


83 


: 84 


76.13 


35.50 


75.97 


35.83 


75.82 


36.16 


75.66 


36.49 


84 


85 


77.04 


35.92 


76.88 


36.26 


76.72 


36.59 


76.56 


36.93 


85 


86 


77.94 


36.35 


77.78 


36.68 


77.62 


37.02 


77.46 


37.38 


86 


87 


78.85 


36.77 


78.69 


37.11 


78.52 


37.45 


78.36 


37.80 


87 


88 


79.76 


37.19 


79.59 


37.54 


79.43 


37.88 


79.26 


38.23 


88 


89 


80.66 


37.61 


80.50 


37.96 


80.33 


38.32 


80.16 


38.67 


89 


90 


81.57 


38.04 


81.40 


38.39 


81.23 


38.75 


81.06 


39.10 


90 


91 


82.47 


38.46 


82.31 


38.82 


82.14 


39.18 


81.96 


39.53 


91 


92 


83.38 


38.88 


83.21 


39.24 


83.04 


39.61 


82.86 


39.97 


92 


93 


84.29 


39.30 


84.11 


39.67 


83.94 


40.04 


83.76 


40.40 


93 


94 


85.19 


39.73 


85.02 


40.10 


84.84 


40.47 


84.67 


40.84 


94 


• 95 


86.10 


40.15 


85.92 


40.52 


85.75 


40.90 


85.57 


41.27 


95 


96 


87.01 


40.57 


86.83 


40.95 


86.65 


41.33 


86.47 


41.71 


96 


97 


87.91 


40.99 


87.73 


41.38 


87.55 


41.76 


87.37 


42.14 


97 


; 98 


88.82 


41.42 


88.64 


41.80 


88.45 


42.19 


88.27 


42.58 


98 


99 


89.72 


41.84 


89.54 


42.23 


89.36 


42.62 


89.17 


43.01 


99 


100 


90.63 


42.26 


90.45 


42.66 


90.26 


43.05 


90.07 


43.44 


100 


a 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Q 


65 ] 


Deg. 


64f 


Deg. 


64J 


Deg. 




643 


Deg. 



54 



TRAVERSE TABLE. 





g 

p 

o 
a 


26 


Deg. 


26} Deg. 


26i 


Deg. 


26| Deg. 


1 






Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 






1 


0.90 


0.44 


0.90 


0.44 


0.89 


0.45 


0.89 


0.45 


1 






2 


1.80 


0.88 


1.79 


0.88 


1.79 


0.89 


1.79 


0.90 


2 






3 


2.70 


1.32 


2.69 


1.33 


2.68 


1.34 


2.68 


1.35 


3 






4 


3.60 


1.75 


3.59 


1.77 


3.58 


1.78 


3.57 


1.80 


4 






5 


4.49 


2.19 


4.48 


2.21 


4.47 


2.23 


4.46 


2.25 


5 






6 


5.39 


2.63 


5.38 


2.65 


5.37 


2.68 


5.36 


2.70 


6 






7 


6.29 


3.07 


6.28 


3.10 


6.26 


3.12 


6.25 


3.15 


7 






8 


7.19 


3.51 


7.17 


3.54 


7.16 


3.57 


7.14 


3.60 


8 






9 


8.09 


3.95 


8.07 


3.98 


8.05 


4.02 


8.04 


4.05 


9 






10 


8.99 


4.38 


8.97 


4.42 


8.95 


4.46 


8.93 


4.50 


10 






Jl 


9.89 


4.82 


9.87 


4.87 


9.84 


4.91 


9.82 


4.95 


11 






12 


10.79 


5.26 


10.76 


5.31 


10.74 


5.35 


10.72 


5.40 


12 






13 


11.68 


5.70 


11.66 


5.75 


11.63 


5.80 


11.61 


5.85 


13 






14 


12.58 


6.14 


12.56 


6.19 


12.53 


6.25 


12.50 


6.30 


14 






15 


13.48 


6.58 


13.45 


6.63 


13.42 


6.69 


13.39 


6.75 


15 






16 


14.38 


7.01 


14.35 


7.08 


14.32 


7.14 


14.29 


7.20 


16 






17 


15.28 


7.45 


15.25 


7.52 


15.21 


7.59 


15.18 


7.65 


17 






18 


16.18 


7.89 


16.14 


7.96 


16.11 


8.03 


16.07 


8.10 


18 






19 


17.08 


8.33 


17.04 


8.40 


17.00 


8.48 


16.97 


8.55 


19 






20 


17.93 


8.77 


17.94 


8.85 


17.90 


8.92 


17.86 


9.00 


20 






21 


18.87 


9.21 


18.83 


9.29 


18.79 


9.37 


18.75 


9.45 


21 






22 


19.77 


9.64 


19.73 


9.73 


19.69 


9.82 


19.65 


9.90 


22 






23 


20.67 


10.08 


20.63 


10.17 


20.58 


10.26 


20.54 


10.35 


23 






24 


21.57 


10.52 


21.52 


10.61 


21.48 


10.71 


21.43 


10.80 


24 






25 


22.47 


10.96 


22.42 


11.06 


22.37 


11.15 


22.32 


11.25 


25 






26 


23.37 


11.40 


23.32 


11.50 


23.27 


11.60 


23.22 


11.70 


26 






27 


24.27 


11.84 


24.22 


11.94 


24.16 


12.05 


24.11 


12.15 


27 






28 


25.17 


12.27 


25.11 


12.38 


25.06 


12.49 


25.00 


12.60 


28 






29 


26.06 


12.71 


26.01 


12.83 


25.95 


12.94 


25.90 


13.05 


29 






30 


26.96 


13.15 


26.91 


13.27 


26.85 


13.39 


26.79 


13.50 


30 






31 


27.86 


13.59 


27.80 


13.71 


27.74 


13.83 


27.68 


13.95 


31 






32 


28.76 


14.03 


28.70 


14.15 


28.64 


14.28 


28.58 


14.40 


32 






33 


29.66 


14.47 


29.60 


14.60 


29.53 


14.72 


29.47 


14.85 


33 






34 


30.56 


14.90 


30.49 


15.04 


30.43 


15.17 


30.36 


15.30 


34 






35 


31.46 


15.34 


31.39 


15.48 


31.32 


15.62 


31.25 


15.75 


35 






36 


32.36 


15.78 


32.29 


15.92 


32.22 


16.06 


32.15 


16.20 


36 






37 


33.26 


16.22 


33.18 


16.36 


33.11 


16.51 


33.04 


16.65 


37 






38 


34.15 


16.66 


34.08 


16.81 


34.01 


16.96 


33.93 


17.10 


38 






39 


35.05 


17.10 


34.98 


17.25 


34.90 


17.40 


34.83 


17.55 


39 






40 


35.95 


17.53 


35.87 


17.69 


35.80 


17.85 


35.72 


18.00 


40 






41 


3G.85 


17.97 


36.77 


18.13 


36.69 


18.29 


36.61 


18.45 


41 






42 


37.75 


18.41 


37.67 


18.58 


37.59 


18.74 


37.51 


18.90 


42 






43 


38.65 


18.85 


38.57 


19.02 


38.48 


19.19 


38.40 


19.35 


43 






44 


39.55 


19.29 


39.46 


19.46 


39.38 


19.63 


39.29 


19.80 


44 






45 


40.45 


19.73 


40.36 


19.90 


40.27 


20.08 


40.18 


20.25 


45 






46 


41.34 


20.17 


41.26 


20.35 


41.17 


20.53 


41.08 


20.70 


46 






47 


42.24 


20.60 


42.15 


20.79 


42.06 


20.97 


41.97 


21.15 


47 






48 


43.14 


21.04 


43.05 


21.23 


42.96 


21.42 


42.86 


21.60 


48 






49 


44.04 


21.48 


43.95 


21.67 


43.85 


21.86 


43.76 


22.05 


49 






50 


44.94 


21.92 


44.84 


22.11 


44.75 


22.31 


44.65 


22.50 


50 






V 

o 
a 

(13 

B 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 


Lat. 


Dep. 


Lat. 


1 






64 1 


)eg. 


63} Deg. 


63J Deg. 


63} Deg. 





TRAVERSE TABLE. 



55 



g 

o 

CD 


26 Deg. 


26} Deg. 


26J Deg. 


26| Deg. 


5 : 

£ 
o 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


45.84 


22.36 


45.74 


22.56 


45.64 


22.76 


45.54 


22.96 


51 1 


52 


46.74 


22.80 


46.64 


23.00 


46.54 


23.20 


46.43 


23.41 


52 I 


53 


47.64 


23.23 


47.53 


23.44 


47.43 


23.65 


47.33 


23.86 


53 \ 


54 


48.53 


23.67 


48.43 


23.88 


48.33 


24.09 


48.22 


24.31 


54 f 


55 


49.43 


24.11 


49.33 


24.33 


49.22 


24.54 


49.11 


24.76 


55 I 


56 


50.33 


24.55 


50.22 


24.77 


50.12 


24.99 


50.01 


25.21 


56 I 


57 


51.23 


24.99 


51.12 


25.21 


51.01 


25.43 


50.90 


25.66 


57 I 


58 


52.13 


25.43 


52.02 


25.65 


51.91 


25.88 


51.79 


26.11 


58 | 


59 


53.03 


25.86 


52.92 


26.09 


52.80 


26.33 


52.69 


26.56 


59 | 


60 


53.93 


26.30 


53.81 


26.54 


53.70 


26.77 


53.58 


27.01 


60 1 


61 


54.83 


26.74 


54.71 


26.98 


54.59 


27.22 


54.47 


27.46 


61 


62 


55.73 


27.18 


55.61 


27.42 


55.49 


27.66 


55.36 


27.91 


62 


63 


56.62 


27.62 


56.50 


27.86 


56.38 


28.11 


56.26 


28.36 


63 


64 


57.52 


28.06 


57.40 


28.31 


57.28 


28.56 


57.15 


28.81 


64 


65 


58.42 


28.49 


58.30 


28.75 


58.17 


29.00 


58.04 


29.26 


65 


66 


59.32 


28.93 


59.19 


29.19 


59.07 


29.45 


58.94 


29.71 


66 


67 


60.22 


29.37 


60.09 


29.63 


59.96 


29.90 


59.83 


30.16 


67 


63 


61.12 


29.81 


60.99 


30.08 


60.86 


30.34 


60.72 


30.61 


68 


69 


62.02 


30.25 


61.88 


30.52 


61.75 


30.79 


61.62 


31.06 


69 


70 


62.92 


30.69 


62.78 


30.96 


62.65 


31.23 


62.51 


31.51 


70 


71 


63.81 


31.12 


63.68 


31.40 


63.54 


31.68 


63.40 


31.96 


71 


72 


64.71 


31.56 


64.57 


31.84 


64.44 


32.13 


64.29 


32.41 


72 


73 


65.61 


32.00 


65.47 


32.29 


65.33 


32.57 


65.19 


32.86 


73 1 


74 


66.51 


32.44 


66.37 


32.73 


66.23 


33.02 


66.08 


33.31 


74 | 


75 


67.41 


32.88 


67.27 


33.17 


67.12 


33.46 


66.97 


33.76 


75 


76 


68.31 


33.32 


68.16 


33.61 


68.01 


33.91 


67.87 


34.21 


76 


77 


69.21 


33.75 


69.06 


34.06 


68.91 


34.36 


68.76 


34.66 


77 | 


78 


70.11 


34.19 


69.96 


34.50 


69.80 


34.80 


69.65 


35.11 


78 I 


79 


71.00 


34.63 


70.85 


34.94 


70.70 


35.25 


70.55 


35.56 


79 


80 


71.90 


35.07 


71.75 


35.38 


71.59 


35.70 


71.44 


36.01 


80 


81 


72.80 


35.51 


72.65 


35.83 


72.49 


36.14 


72.33 


36.46 


81 


82 


73.70 


35.95 


73.54 


36.27 


73.38 


36.59 


73.22 


36.91 


82 


83 


74.60 


36.38 


74.44 


36.71 


74.28 


37.03 


74.12 


37.36 


83 


84 


75.50 


36.82 


75.34 


37.15 


75.17 


37.48 


75.01 


37.81 


84 


85 


76.40 


37.26 


76.23 


37.59 


76.07 


37.93 


75.90 


38.26 


85 


86 


77.30 


37.70 


77.13 


38.04 


76.96 


38.37 


76.80 


38.71 


86 


87 


78.20 


38.14 


78.03 


38.48 


77.86 


38.82 


77.69 


39.16 


88 


88 


79.09 


38.58 


78.92 


38.92 


78.75 


39.27 


78.58 


39.61 


89 


79.99 


39.01 


79.82 


39.36 


79.65 


39.71 


79.48 


40.06 


89 | 


90 


80.89 


39.45 


80.72 


39.81 


80.54 


40.16 


80.37 


40.51 


90 S 


91 


81.79 


39.89 


81.62 


40.25 


81.44 


40.60 


81.26 


40.96 


91 


92 


82.69 


40.33 


82.51 


40.69 


82.33 


41.05 


82.15 


41.41 


92 I 


93 


83.59 


40.77 


83.41 


41.13 


83.23 


41.50 


83.05 


41.86 


93 I 


94 


84.49 


41.21 


84.31 


41.58 


84.12 


41.94 


83.94 


42.31 


94 § 


95 


85.39 


41.65 


85.20 


42.02 


85.02 


42.39 


84.83 


42.76 


95 f 


96 


86.28 


42.08 


86.10 


42.46 


85.91 


42.83 


85.73 


43.21 


96 I 


97 


87.18 


42.52 


87.00 


42.90 


86.81 


43.28 


86.62 


43.66 


97 1 


98 


88.08 


42.96 


87.89 


43.34 


87.70 


43.73 


87.51 


44.11 


98 


99 


88.98 


43.40 


88.79 


43.79 


88.60 


44.17 


88.40 


44.56 


99 


100 

3 


89.88 


43.84 


89.69 


44.23 


89.49 


44.62 


89.30 


45.01 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


e 

ft 

.a 

Q 


64 1 


>g. 


63| 


Deg. 


634 Deg. 


63* Deg. 



56 



TRAVERSE TABLE. 



a 

a 

9 


2? Deg. 


27* Deg. 


27i 


Deg. 


27| Deg. 


O t 
° 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.89 


0.45 


9. 89 


0.46 


0.89 


0.46 


0.88 


0.47 


1 


2 


1.78 


0.91 


1.78 


0.92 


1.77 


0.92 


1.77 


0.93 


2 


3 


2.67 


1.36 


2.67 


1.37 


2.66 


1.39 


2.65 


1.40 


3 


4 


3.56 


1.82 


3.56 


1.83 


3.55 


1.85 


3.54 


1.86 


4 


5 


4.45 


2.27 


4.45 


2.29 


4.44 


2.31 


4.42 


2.33 


5 [ 


6 


5.35 


2.72 


5.33 


2.75 


5.32 


2.77 


5.31 


2.79 


6 


7 


6.24 


3.18 


S.22 


3.21 


6.21 


3.23 


6.19 


3.26 


7 


8 


7.13 


3.63 


7.11 


3.66 


7.10 


3.69 


7.08 


3.72 


8 


9 


8.02 


4.09 


8.00 


4.12 


7.98 


4.16 


7.96 


4.19 


9 


10 


8.91 


4.54 


8.89 


4.58 


8.87 


4.62 


8.85 


4.66 


10 


11 


9.80 


4.99 


9.78 


5.04 


9.76 


5.08 


9.73 


5.12 


11 1 

12 1 


12 


10.69 


5.45 


10.67 


5.49 


10.64 


5.54 


10.62 


5.59 


13 


11.58 


5.90 


11.56 


5.95 


11.53 


6.00 


11.50 


6.05 


13 ; 


14 


12.47 


6.36 


12.45 


6.41 


12.42 


6.46 


12.39 


6.52 


14 


15 


13.37 


6.81 


13.34 


6.87 


13.31 


6.93 


13.27 


6.98 


15 


16 


14.26 


7.26 


14.22 


7.33 


14.19 


7.39 


14.16 


7.45 


16 


17 


15.15 


7.72 


15.11 


7.78 


15.08 


7.85 


15.04 


7.92 


17 | 


18 


16.04 


8.17 


16.00 


8.24 


15.97 


8.31 


15.93 


8.38 


18 


19 


16.93 


8.63 


16.89 


8.70 


16.85 


8.77 


16.81 


8.85 


19 


20 


17.82 


9.08 


17.78 


9.16 


17.74 


9.23 


17.70 


9.31 


20 


21 


13.71 


9.53 


18.67 


9.62 


18.63 


9.70 


18.58 


9.78 


21 


22 


19.60 


9.99 


19.56 


10.07 


19.51 


10.16 


19.47 


10.24 


22 


23 


20.49 


10.44 


20.45 


10.53 


20.40 


10.62 


20.35 


10.71 


23 


24 


21.38 


10.90 


21.34 


10.99 


21.29 


11.08 


21.24 


11.17 


24 


25 


22.28 


11.35 


22.23 


11.45 


22.18 


11.54 


22.12 


11.64 


25 


26 


23.17 


11.80 


23.11 


11.90 


23.06 


12.01 


23.01 


12.11 


26 


27 


24.06 


12.26 


24.00 


12.36 


23.95 


12.47 


23.89 


12.57 


27 


28 


24.95 


12.71 


24.89 


12.82 


24.84 


12.93 


24.78 


13.04 


28 


29 


25.84 


13.17 


25.78 


13.28 


25.72 


13.39 


25.66 


13.50 


29 


30 


26.73 


13.62 


26.67 


13.74 


26.61 


13.85 


26.55 


13.97 


30 


31 


27.62 


14.07 


27.56 


14.19 


27.50 


14.31 


27.43 


14.43 


31 


32 


28.51 


14.53 


28.45 


14.65 


28.38 


14.78 


28.32 


14.90 


32 


33 


29.40 


14.93 


29.34 


15.11 


29.27 


15.24 


29.20 


15.37 


33 


34 


30.29 


15.44 


30.23 


15.57 


30.16 


15.70 


30.09 


15.83 


34 


35 


31.19 


15.89 


31.12 


16.03 


31.05 


16.16 


30.97 


16.30 


35 


36 


32.08 


16.34 


32.00 


16.48 


31.93 


16.62 


31.86 


16.76 


36 
37 


37 


32.97 


16.80 


32.89 


16.94 


32.82 


17.08 


32.74 


17.23 


38 


33.86 


17.25 


33.78 


17.40 


33.71 


17.55 


33.63 


17.69 


38 


39 


34.75 


17.71 


34.67 


17.86 


34.59 


18.01 


34.51 


18.16 


39 


40 


35.64 


18.16 


35.56 


18.31 


35.48 


18.47 


35.40 


13.62 


'10 


41 


36.53 


18.61 


36.45 


18.77 


36.37 


18.93 


36.28 


19.09 


-11 


42 


37.42 


19.07 


37.34 


19.23 


37.25 


19.39 


37.17 


19.56 


42 


43 


38.31 


19.52 


38.23 


19.69 


38.14 


19.86 


33.05 


20.02 


43 


44 


39.20 


19.98 


39.12 


20.15 


39.03 


20.32 


38.94 


20.49 


44 


45 


40.10 


20.43 


40.01 


20.60 


39.92 


20.78 


39.82 


20.95 


45 


46 


40.99 


20.88 


40.89 


21.06 


40.80 


21.24 


40.71 


21.42 


46 


47 


41.88 


21.34 


41.78 


21.52 


41.69 


21.70 


41.59 


21.88 


47 


48 


42.77 


21.79 


42.67 


21.98 


42.58 


22.16 


42.48 


22.35 


48 


49 


43.66 


22.25 


43.56 


22.44 


43.46 


22.63 


43.36 


22.82 


49 


50 


44.55 


22.70 


44.45 


22.89 


44.35 


23.09 


44.25 


23.23 


50 


gS 

o 

£3 

S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 



- 

a 


63 1 


)eg. 


62| 


Deg. 


62$ 


Deg. 


62* 


Deg. 



TRAVERSE TABLE. 



57 





27 Deg. 


27i Deg. 


27* Deg. 


27J Deg. 


O 

p 
o 
a 


o 

CO 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 Dep. 


51 


45.44 


23.15 


45.34 


23.35 


45.24 


23.55 


45.13 


23.75 


51 


52 


46.33 


23.61 


46.23 


23.81 


46.12 


24.01 


46.02 


24.21 


52 


53 


47.22 


24.06 


47.12 


24.27 


47.01 


24.47 


46.90 


24.68 


53 


54 


48.11 


24.52 


48.01 


24.73 


47.90 


24.93 


47.79 


25.14 


54 


55 


49.01 


24.97 


48.90 


25.18 


48.79 


25.40 


48.67 


25.61 


55 


56 


49.90 


25.42 


49.78 


25.64 


49.67 


25.86 


49.56 


26.07 


56 


57 


50.79 


25.88 


50.67 


26.10 


50.56 


26.32 


50.44 


26.54 


57 


58 


51.68 


26.33 


51.56 


26.56 


51.45 


26.78 


51.33 


27.01 


58 


59 


52.57 


26.79 


52.45 


27.01 


52.33 


27.24 


52.21 


27.47 


59 


60 


53.46 


27.24 


53.34 


27.47 


53.22 


27.70 


53.10 


27.94 


60 


61 


54.35 


27.69 


54.23 


27.93 


54.11 


28.17 


53.98 


28.40 


61 


62 


55.24 


28.15 


55.12 


28.39 


54.99 


28.63 


54.87 


28.87 


62 


63 


56.13 


28.60 


56.01 


28.85 


55.88 


29.09 


55.75 


29.33 


63 


64 


57.02 


29.06 


56.90 


29.30 


56.77 


29.55 


56.64 


29.80 


64 


65 


57.92 


29.51 


57.79 


29.76 


57.66 


30.01 


57.52 


30.26 


65 


66 


58.81 


29.96 


58.68 


30.22 


58.54 


30.48 


58.41 


30.73 


66 


67 


59.70 


30.42 


59.56 


30.68 


59.43 


30.94 


59.29 


31.20 


67 


68 


60.59 


30.87 


60.45 


31.14 


60.32 


31.40 


60.18 


31.66 


68 


69 


61.48 


31.33 


61.34 


31.59 


61.20 


31.86 


61.06 


32.13 


69 


70 


62.37 


31.78 


62.23 


32.05 


62.09 


32.32 


61.95 


32.59 


70 


71 


63.26 


32.23 


63.12 


32.51 


62.98 


32.78 


62.83 


33.06 


71 


72 


64.15 


32.69 


64.01 


32.97 


63.86 


33.25 


63.72 


33.52 


72 


73 


65.04 


33.14 


64.90 


33.42 


64.75 


33.71 


64.60 


33.99 


73 


74 


65.93 


33.60 


65.79 33.88 


65.64 


34.17 


65.49 


34.46 


74 


75 


66 83 


34.05 


66.68 34.34 


66.53 


34.63 


66.37 


34.92 


75 


76 


67.72 


34.50 


67.57 


34.80 


67.41 


35.09 


67.26 


35.39 


76 


77 


68.61 


34.96 


68.45 


35.26 


68.30 


35.55 


68.14 


35.85 


77 


78 


69.50 


35.41 


69.34 


35.71 


69.19 


36.02 


69-03 


36.32 


78 


79 


70.39 


35.87 


70.23 


36.17 


70.07 


36.48 


69.91 


36.78 


79 


80 


71.28 


36.32 


71.12 


36.63 


70.96 


36.94 


70.80 


37.25 


80 


81 


72.17 


36.77 


72.01 


37.09 


71.85 


37.40 


71.63 


37.71 


81 


82 


73.06 


37.23 


72.90 


37.55 


72.73 


37.86 


72.57 


38.18 


82 


83 


73.95 


37.68 


73.79 


38.00 


73.62 


38.33 


73.45 


38.65 


83 


84 


74.84 


38.14 


74.68 


33.46 


74.51 


38.79 


74.34 


39.11 


84 


85 


75.74 


38.59 


75.57 


38.92 


75.40 


39.25 


75.22 


39.58 


85 


88 


76.63 


39.04 


76.46 


39.38 


76.28 


39.71 


76.11 


40.04 


86 


87 


77.52 


39.50 


77.34 


39.83 


77.17 


40.17 


76.99 


40.51 


87 


88 


78.41 


39.95 


78.23 


40.29 


78.06 


40.63 


77.88 


40.97 


88 


89 


79.30 


40.41 


79.12 


40.75 


78.94 


41.10 


78.76 


41.44 


89 


90 


80.19 


40.86 


80.01 


41.21 


79.83 


41.56 


79.65 


41.91 


90 


91 


81.08 


41.31 


80.90 


41.67 


80.72 


42.02 


80.53 


42.37 


91 


92 


81.97 


41.77 


81.79 


42.12 


81.60 


42.48 


81.42 


42.84 


92 


93 


82.86 


42.22 


82.62 


42.58 


82.49 


42.94 


82.30 


43.30 


93 


94 


83.75 


42.68 


83.57 


4<*.04 


83.38 


43.40 


83.19 


43.77 


94 | 


95 


84.65 


43.13 


84.46 


43. d0 


84.27 


43.87 


84.07 


44.23 


95 


96 


85.54 


43.58 


85.35 


43.96 


85.15 


44.33 


84.96 


44.70 


96 


97 


86.43 


44.04 


86.23 


44.41 


86.04 


44.79 


85.84 


45.16 


97 


98 


87.32 


44.49 


87.12 


44.87 


86.93 


45.25 


86.73 


45.63 


98 


99 


88.21 


44.95 


88.01 


45.33 


87.81 


45.71 


87.61 


46.10 


99 


100 


89.10 


45.40 


88.90 


45.79 


88.70 


46.17 


88.50 


46.56 


100 


a 
5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




63 Deg. 


62| Deg. 


62i Deg. 


62* Deg. 



29 



2U 



58 



'RAVERSE TABLE. 



O 

U 

3 
O 


28 Deg. 


28* Deg. 


28i Deg. 


28| Deg. 


3 
O 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.88 


0.47 


0.88 


0.47 


0.88 


0.48 


0.88 


0.48 


1 


2 


1.77 


0.94 


1.76 


0.95 


1.76 


0.95 


1.75 


0.96 


2 


3 


2.65 


1.41 


2.64 


1.42 


2.64 


1.43 


2.63 


1.44 


3 


4 


3.53 


1.88 


3.52 


1.89 


3.52 


1.91 


3.51 


1.92 


4 


5 


4.41 


2.35 


4.40 


2.37 


4.39 


2.39 


4.38 


2.40 


5 


6 


5.30 


2.82 


5.29 


2.84 


5.27 


2.86 


5.26 


2.89 


6 


7 


6.18 


3.29 


6.17 


3.31 


6.15 


3.34 


6.14 


3.37 


7 


8 


7.06 


3.76 


7.05 


3.79 


7.03 


3.82 


7.01 


3.85 


8 


9 


7.95 


4.23 


7.93 


4.26 


7.91 


4.29 


7.89 


4.33 


9 


10 


8.83 


4.69 


8.81 


4.73 


8.79 


4.77 


8.77 


4.81 


10 


11 


9.71 


5.16 


9.69 


5.21 


9.67 


5.25 


9.64 


5.29 


11 


12 


10.60 


5.63 


10.57 


5.68 


10.55 


5.73 


10.52 


5.77 


12 


13 


11.48 


6.10 


11.45 


6.15 


11.42 


6.20 


11.40 


6.25 


13 


14 


12.36 


6.57 


12.33 


6.63 


12.30 


6.68 


12.27 


6.73 


14 


15 


13.24 


7.04 


13.21 


7.10 


13.18 


7.16 


13.15 


7.21 


15 


16 


14.13 


7.51 


14.09 


7.57 


14.06 


7.63 


14.03 


7.70 


16 


17 


15.01 


7.98 


14.98 


8.05 


14.94 


8.11 


14.90 


8.18 


17 


13 


15.89 


8.45 


15.86 


8.52 


15.82 


8.59 


15.78 


8.66 


18 


19 


16.78 


8.92 


16.74 


8.99 


16.70 


9.07 


16.66 


9.14 


19 


20 


17.66 


9.39 


17.62 


9.47 


17.58 


9.54 


17.53 


9.62 


20 


21 


18.54 


9.86 


18.50 


9.94 


18.46 


10.02 


18.41 


10.10 


21 


22 


19.42 


10.33 


19.38 


10.41 


19.33 


10.50 


19.29 


10.58 


22 


23 


20.31 


10.80 


20.26 


10.89 


20.21 


10.97 


20.16 


11.06 


23 


24 


21.19 


11.27 


21.14 


11.36 


21.09 


11.45 


21.04 


11.54 


24 


25 


22.07 


11.74 


22.02 


11.83 


21.97 


11.93 


21.92 


12.02 


25 


26 


22.96 


12.21 


22.90 


12.31 


22.85 


12.41 


22.79 


12.51 


26 


27 


23.84 


12.68 


23.78 


12.78 


23.73 


12.88 


23.67 


12.99 


27 


28 


24.72 


13.15 


24.66 


13.25 


24.61 


13.36 


24.55 


13.47 


28 


29 


25.61 


13.61 


25.55 


13.73 


25.49 


13.84 


25.43 


13.95 


29 


30 


26.49 


14.08 


26.43 


14.20 


26.36 


14.31 


26.30 


14.43 


30 


31 


27.37 


14.55 


27.31 


14.67 


27.24 


14.79 


27.18 


14.91 


31 


32 


28.25 


15.02 


28.19 


15.15 


28.12 


15.27 


28.06 


15.39 


32 


33 


29.14 


15.49 


29.07 


15.62 


29.00 


15.75 


28.93 


15.87 


33 


34 


30.02 


15.96 


29.95 


16.09 


29.88 


16.22 


29.81 


16.35 


34 


35 


30.90 


16.43 


30.83 


16.57 


30.76 


16.70 


30.69 


16.83 


35 


36 


31.79 


16.90 


31.71 


17.04 


31.64 


17.18 


31.56 


17.32 


36 


37 


32.67 


17.37 


32.59 


17.51 


32.52 


17.65 


32.44 


17.80 


37 


38 


33.55 


17.84 


33.47 


17.99 


33.39 


18.13 


33.32 


18.28 


38 


39 


34.43 


18.31 


34.35 


18.46 


34.27 


18.61 


34.19 


18.76 


39 


40 


35.32 


18.73 


35.24 


18.93 


35.15 


19.09 


35.07 


19.24 


40 


41 


36.20 


19.25 


36.12 


19.41 


36.03 


19.56 


35.95 


19.72 


41 


42 


37.03 


19.72 


37.00 


19.88 


36.91 


20.04 


36.82 


20.20 


42 


43 


37.97 


20.19 


37.88 


20.35 


37.79 


20.52 


37.70 


20.68 


43 


44 


38.85 


20.66 


38.76 


20.83 


38.67 


20.99 


38.58 


21.16 


44 


45 


39.73 


21.13 


39.64 


21.30 


39. 5 C 


21.47 


39.45 


21.64 


45 


46 


40.62 


21.60 


40.52 


21.77 


40.43 


21.95 


40.33 


22.13 


46 


47 


41.50 


22.07 


41.40 


22.25 


41.30 


22.43 


41.21 


22.61 


47 


43 


42.38 


22.53 


42.28 


22.72 


42.18 


22.90 


42.08 


23.09 ! 48 


49 


43.26 


23.00 


43.16 


23.19 


43.06 


23.38 


42.96 


23.57 


49 


50 


44.15 


23.47 


44.04 


23.67 


43.94 


23.86 


43.84 


24.05 


50 


B 

O 

c 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 


Lat. 


e 
u 
a 
I 

i 


62 1 


fcg. 


61! 


Deg. 


61J 


Deg. 


61* Deg. 



TRAVERSE TABLE. 



59 



o 

s 
o 
? 


28 Deg. 


28i 


Beg. 


28i Deg. 


28| Deg. 


g 

H : 

o 

re 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


45.03 


23.94 


44.93 


24.14 


44.82 


24.34 


44.71 


24.53 


51 


52 


45.91 


24.41 


45.81 


24.61 


45.70 


24.81 


45.59 


25.01 


52 
53 


53 


46.80 


24.88 


46.69 


25.09 


46.58 


25.29 


46.47 


25.49 


54 


47.68 


25.35 


47.57 


25.56 


47.46 


25.77 


47.34 


25.97 


54 


55 


48.56 


25.82 


48.45 


26.03 


48.33 


26.24 


48.22 


26.45 


55 

56 ' 


56 


49.45 


26.29 


49.33 


26.51 


49.21 


26.72 


49.10 


26.94 


57 


50.33 


26.76 


50.21 


26.98 


50.09 


27.20 


49.97 


27.42 


57 


58 


51.21 


27.23 


51.09 


27.45 


50.97 


27.68 


50.85 


27.90 


58 


59 


52.09 


27.70 


51.97 


27.93 


51.85 


28.15 


51.73 


28.38 


59 


60 


52.98 


28.17 


52.85 


28.40 


52.73 


28.63 


52.60 


28.86 


60 


61 


53.86 


28.64 


53.73 


28.87 


53.61 


29.11 


53.48 


29.34 


61 


62 


54.74 


29.11 


54.62 


29.35 


54.49 


29.58 


54.36 


29.82 


62 


63 


55.63 


29.58 


55.50 


29.82 


55.37 


30.06 


55.23 


30.30 


63 


64 


56.51 


30.05 


56.38 


30.29 


56.24 


30.54 


56.11 


30.78 


64 


65 


57.39 


30.52 


57.26 


30.77 


57.12 


31.02 


56.99 


31.26 


65 


66 


58.27 


30.99 


58.14 


31.24 


58.00 


31.49 


57.86 


31.75 


66 


67 


59.16 


31.45 


59.02 


31.71 


58.88 


31.97 


58.74 


32.23 


67 


68 


60.04 


31.92 


59.90 


32.19 


59.76 


32.45 


59.62 


32.71 


68 


69 


60.92 


32.39 


60.78 


32.66 


60.64 


32.92 


60.49 


33.19 


69 


70 


61.81 


32.86 


61.66 


33.13 


61.52 


33.40 


61.37 


33.67 


70 


71 


62.69 


33.33 


62.54 


33.61 


62.40 


33.88 


62.25 


34.15 


71 


72 


63.57 


33.80 


63.42 


34.08 


63.27 


34.36 


63.12 


34.63 


72 


73 


64.46 


34.27 


64.30 


34.55 


64.15 


34.83 


64.00 


35.11 


73 


74 


65.34 


34.74 


65.19 


35.03 


65.03 


35.31 


64.88 


35.59 


74 


75 


66.22 


35.21 


66.07 


35.50 


65.91 


35.79 


65.75 


36.07 


75 


76 


67.10 


35.68 


66.95 


35.97 


66.79 


36.26 


66.63 


36.56 


76 ■ 


77 


67.99 


36.15 


67.83 


36.45 


67.67 


36.74 


67.51 


37.04 


77 


78 


68.87 


36.62 


68.71 


36.92 


68.55 


37.22 


68.38 


37.52 


78 


79 


69.75 


37.09 


69.59 


37.39 


69.43 


37.70 


69.26 


38.00 


79 


80 


70.64 


37.56 


70.47 


37.87 


70.31 


38.17 


70.14 


38.48 


80 


81 


71.52 


38.03 


71.35 


38.34 


71.18 


38.65 


71.01 


38.96 


81 


82 


72.40 


38.50 


72.23 


38.81 


72.06 


39.13 


71.89 


39.44 


82 


83 


73.28 


38.97 


73.11 


39.29 


72.94 


39.60 


72.77 


39.92 


83 


84 


74.17 


39.44 


73.99 


39.76 


73.82 


40.08 


73.64 


40.40 


84 


85 


75.05 


39.91 


74.88 


40.23 


74.70 


40.56 


74.52 


40.88 


85 


86 


75.93 


40.37 


75.76 


40.71 


75.58 


41.04 


75.40 


41.36 


86 


87 


76.82 


40.84 


76.64 


41.18 


76.46 


41.51 


76.28 


41.85 


87 


88 


77.70 


41.31 


77.52 


41.65 


77.34 


41.99 


77.15 


42.33 


88 


89 


78.58 


41.78 


78.40 


42.13 


78.21 


42.47 


78.03 


42.81 


89 


90 


79.47 


42.25 


79.28 


42.60 


79.09 


42.94 


78.91 


43.29 


90 


91 


80.35 


42.72 


80.16 


43.07 


79.97 


43.42 


79.78 


43.77 


91 


92 


81.23 


43.19 


81.04 


43.55 


80.85 


43.90 


80.66 


44.25 


92 


93 


82.11 


43.66 


81.92 


44.02 


81.73 


44.38 


81.54 


44.73 


93 


94 


83.00 


44.13 


82.80 


44.49 


82.61 


44.85 


82.41 


45.21 


94 


95 


83.88 


44.60 


83.68 


44.97 


83.49 


45.33 


83.29 


45.69 


95 


96 


84.76 


45.07 


84.57 


45.44 


84.37 


45.81 


84.17 


46.17 


96 


97 


85.65 


45.54 


85.45 


45.91 


85.25 


46.28 


85.04 


46.66 


97 


98 


86.53 


46.01 


86.33 


46.39 


86.12 


46.76 


85.92 


47.14 


98 


99 


87.41 


46.48 


87.21 


46.86 


87.00 


47.24 


86.80 


47.62 


99 


100 


88.29 


46.95 


88.09 


47.33 


87.88 


47.72 


87.67 


48.10 


100 


i 

o 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a 
a 

a 

Q 


62 ] 


3eg. 


61* 


Deg. 


61 J Deg. 


6U Deg. 



bo 



TRAVERSE TABLE. 





Is 

1 

CD 
1 


29 Deg. 


294 Deg. 


29* 


Deg. 


29} Deg. 




& 

3 
O 
? 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




0.87 


0.48 


0.87 


0.49 


0.87 


0.49 


0.87 


0.50 


1 




2 


1.75 


0.97 


1.74 


0.98 


1.74 


0.98 


1.74 


0.99 


2 




3 


2.62 


1.45 


2.62 


1.47 


2.61 


1.48 


2.60 


1.49 


3 




4 


3.50 


1.94 


3.49 


1.95 


3.48 


1.97 


3.47 


1.98 


4 




5 


4.37 


2.42 


4.36 


2.44 


4.35 


2.46 


4.34 


2.48 


5 




6 


5.25 


2.91 


5.23 


2.93 


5.22 


2.95 


5.21 


2.98 


6 




7 


6.12 


3.39 


6.11 


3.42 


6.09 


3.45 


6.08 


3.47 


7 




8 


7.00 


3.88 


6.98 


3.91 


6.96 


3.94 


6.95 


3.97 


8 




9 


7.87 


4.36 


7.85 


4.40 


7.83 


4.43 


7.81 


4.47 


9 




10 


8.75 


4.85 


8.72 


4.89 


8.70 


4.92 


8.68 


4.96 


10 




11 


9.62 


5.33 


9.60 


5.37 


9.57 


5.42 


9.55 


5.46 


11 




12 


10.50 


5.82 


10.47 


5.86 


10.44 


5.91 


10.42 


5.95 


12 




13 


11.37 


6.30 


11.34 


6.35 


11.31 


6.40 


11.29 


6.45 


13 




14 


12.24 


6.79 


12.21 


6.84 


12.18 


6.89 


12.15 


6.95 


14 




15 


13.12 


7.27 


13.09 


7.33 


13.06 


7.39 


13.02 


7.44 


15 ' 




16 


13.99 


7.76 


13.96 


7.82 


13.93 


7.88 


13.89 


7.94 


16 




17 


14.87 


8.24 


14.83 


8.31 


14.80 


8.37 


14.76 


8.44 


17 




18 


15.74 


8.73 


15.70 


8.80 


15.67 


8.86 


15.63 


8.93 


18 




19 


16.62 


9.21 


16.58 


9.28 


16.54 


9.36 


16.50 


9.43 


19 




20 


17.49 


9.70 


17.45 


9.77 


17.41 


9.85 


17.36 


9.92 


20 




21 


18.37 


10.18 


13.32 


10.26 


18.28 


10.34 


18.23 


10.42 


21 




22 


19.24 


10.67 


19.19 


10.75 


19.15 


10.83 


19.10 


10.92 


22 




23 


20.12 


11.15 


20.07 


11.24 


20.02 


11.33 


19.97 


11.41 


23 




24 


20.99 


11.64 


20.94 


11.73 


20.89 


11.82 


20.84 


11.91 


24 




25 


21.87 


12.12 


21.81 


12.22 


21.76 


12.31 


21.70 


12.41 


25 




26 


22.74 


12.60 


22.68 


12.70 


22.63 


12.80 


22.57 


12.90 


26 




27 


23.61 


13.09 


23.56 


13.19 


23.50 


13.30 


23.44 


13.40 


27 




28 


24.49 


13.57 


24.43 


13.63 


24.37 


13.79 


24.31 


13.89 


28 




29 


25.36 


14.06 


25.30 


14.17 


25.24 


14.28 


25.18 


14.39 


29 




30 


26.24 


14.54 


26.17 


14.66 


26.11 


14.77 


26.05 


14.89 


30 




31 


27.11 


15.03 


27.05 


15.15 


26.98 


15.27 


26.91 


15.38 


31 




32 


27.99 


15.51 


27.92 


15.64 


27.85 


15.76 


27.78 


15.88 


32 




33 


28.86 


16.00 


28.79 


16.12 


28.72 


16.25 


28.65 


16.38 


33 




34 


29.74 


16.48 


29.66 


16.61 


29.59 


16.74 


29.52 


16.87 


34 




35 


30.61 


16.97 


30.54 


17.10 


30.46 


17.23 


30.39 


17.37 


35 




36 


31.49 


17.45 


31.41 


17.59 


31.33 


17.73 


31.26 


17.86 


36 




37 


32.36 


17.94 


32.28 


18.08 


32.20 


18.22 


32.12 


18.36 


37 




38 


33.24 


18.42 


33.15 


18.57 


33.07 


18.71 


32.99 


13.86 


38 




39 


34.11 


18.91 


34.03 


19.66 


33.94 


19.20 


33.86 


19.35 


39 




40 


34.98 


19.39 


34.90 


19.54 


34.81 


19.70 


34.73 


19.85 


40 




41 


35.86 


19.88 


35.77 


20.03 


35.68 


20.19 


35.60 


20.34 


41 




42 


36.73 


20.36 


36.64 


20.52 


36.55 


20.68 


36.46 


20.84 


42 




43 


37.61 


20.85 


37.52 


21.01 


37.43 


21.17 


37.33 


21.34 


43 




44 


38.48 


21.33 


38.39 


21.50 


38-30 


21.67 


38.20 


21.83 


44 




45 


39.36 


21.82 


39.26 


21.99 


39.17 


22.16 


39.07 


22.33 


45 




46 


40.23 


22.30 


40.13 


22.48 


40.04 


22.65 


39.94 


22.83 


46 




47 41.11 


22.79 


41.01 


22.97 


40.91 


23.14 


40.81 


23.32 


47 




48 


41.98 


23.27 


41.88 


23.45 


41.78 


23.63 


41.67 


23.82 


48 




49 


42.86 


23.76 


42.75 


23.94 


42.65 


24.13 


42.54 


24.31 


49 




50 


43.73 


24.24 


43.62 


24.43 


43.52 


24.62 


43.41 


24.81 


50 




g 
i 

-a 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 

a 

Q 




61 I 


)eg. 


60J Deg. 


60i Deg. 


604 


Deg. 



TRAVERSE TABLE 



61 



b 

ST 

a 
a 
? 


29 Deg. 


29* Deg. 


29* Deg. 


29| Deg. 


fl 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


44.61 


24.73 


44.50 


24.92 


44.39 


25.11 


44.28 


25.31 


51 


52 


45.48 


25.21 


45.37 


25.41 


45.26 


25.61 


45.15 


25.80 


52 


53 


46.35 


25.69 


46.24 


25.90 


1 46.13 


26.10 


46.01 


26.30 


53 


54 


47.23 


26.18 


47.11 


26.39 


47.00 


26.59 


46.88 


26.80 


54 


55 


48.10 


26.66 


47.99 


26.87 


47.87 


27.08 


47.75 


27.29 


55 


56 


48-98 


27.15 


48.86 


27.36 


48.74 


27.58 


48.62 


27.79 


56 


57 


49.85 


27.63 


49.73 


27.85 


49.61 


28.07 


49.49 


28.28 


51 


58 


50.73 


28.12 


50.60 


28.34 


50.48 


28.56 


50.36 


28.78 


58 


59 


51.60 


28.60 


51.48 


28.83 


51.35 


29.05 


51.22 


29.28 


59 


60 


52.48 


29.09 


52.35 


29.32 


52.22 


29.55 


52.09 


29.77 


60 


61 


53-35 


29.57 


53.22 


29.81 


53.09 


30.04 


52.96 


30.27 


61 


62 


54.23 


30.06 


54.09 


30.29 


53.96 


30.53 


53.83 


30.77 


62 


63 


55.10 


30.54 


54.97 


30.78 


54.83 


31.02 


54.70 


31.26 


63 


64 


55.98 


31.03 


55.84 


31.27 


55.70 


31.52 


55.56 


31.76 


64 


65 


56.85 


31.51 


56.71 


31.76 


56.57 


32.01 


56.43 


32.25 


65 


66 


57.72 


32.00 


57.58 


32.25 


57.44 


32.50 


57.30 


32.75 


m 


67 


58.60 


32.48 


58.46 


32.74 


58.31 


32.99 


58.17 


33-25 


67 


68 


59.47 


32.97 


59.33 


33.23 


59.18 


33.48 


59.04 


33.74 


68 


69 


60.35 


33.45 


60.20 


33.71 


60.05 


33.98 


59.91 


34.24 


69 


70 


61.22 


33.94 


61.07 


34.20 


60.92 


34.47 


60.77 


34.74 


70 


71 


62.10 


34.42 


61.95 


34.69 


61.80 


34.96 


61.64 


35.23 


71 


72 


62.97 


34.91 


62.82 


35.18 


62.67 


35.45 


62.51 


35.73 


72 


73 


63.85 


35.39 


63.69 


35.67 


63.54 


35.95 


63.38 


36.22 


73 


74 


64.72 


35.88 


64.56 


36.16 


64.41 


36.44 


64.25 


36.72 


74 


75 


65.60 


36-36 


65.44 


36.65 


65.28 


36.93 


65.11 


37.22 


75 


76 


66.47 


36-85 


66.31 


37.14 


66.15 


37.42 


65.98 


37.71 


76 


77 


67.35 


37.33 


67.18 


37.62 


67.02 


37.92 


66.85 


38.21 


77 


78 


68.22 


37.82 


68.05 


38.11 


67.89 


38.41 


67.72 


38.70 


78 


79 


69.09 


38.30 


68.93 


38.60 


68.76 


38-90 


68.59 


39.20 


79 


80 


69.97 


38.78 


69.80 


39.09 


69.63 


39.39 


69.46 


39.70 


80 


81 


70.84 


39.27 


70.67 


39.58 


70.50 


39.89 


70.32 


40.19 


81 


82 


71.72 


39.75 


71.54 


40.07 


71.37 


40.38 


71.19 


40.69 


82 


83 


72.59 


40.24 


72.42 


40.56 


72.24 


40.87 


72.06 


41.19 


83 


84 


73.47 


40.72 


73.29 


41.04 


73.11 


41.36 


72.93 


41.68 


84 


85 


74.34 


41.21 


74.16 


41.53 


73.98 


41.86 


73-80 


42.18 


85 


86 


75.22 


41.69 


75.03 


42.02 


74.85 


42.35 


74.67 


42.67 


86 


87 


76.09 


42.18 


75.91 


42.51 


75.72 


42.84 


75.53 


43.17 


87 


88 


76.97 


42-66 


76.78 


43.00 


76.59 


43.33 


76.40 


43.67 


88 


89 


77.84 


43.15 


77.65 


43.49 


77.46 


43.83 


77.27 


44.16 


89 


90 


78.72 


43.63 


78.52 


43.98 


78.33 


44.32 


78.14 


44.66 


90 


91 


79.59 


44.12 


79.40 


44.46 


79.20 


44.81 


79.01 


45.16 


91 


92 


80.46 


44.60 


80.27 


44.95 


80.07 


45.30 


79.87 


45.65 


92 


93 
94 


81.34 


45-09 


81.14 


45.44 


80.94 


45.80 


80.74 


46.15 


93 


82.21 


45.57 


82-01 


45.93 


81.81 


46.29 


81.61 


46.64 


94 


95 83.09 


46.06 


82.89 


46.42 


82.68 


46.78 


82.48 


47.14 


95 


96 


83.96 


46.54 


83.76 


46.91 


83.55 


47.27 


83.35 


47.64 


96 


97 


84.84 


47.03 


84.63 


47.40 


84.42 


47.77 


84.22 


48.13 


97 


98 


85.71 


47.51 


85.50 


47.88 


85.29 


48.26 


85.08 


48.63 


98 


99 


86.59 


48.00 


86.38 


48.37 


86.17 


48.75 


85.95 


49.13 


99 


100 


87.46 


48.48 


87.25 


48.86 


87.04 


49.24 


86.82 


49.62 


100 


a 
£ 

Q 

• 


Dep. 


Lat. 


Dep. 


Lat 


Dep. 


Lat. 


Dep. 


Lat. 


• 

o 

c 

5 


611 


)eg. 


60| D«g. 


60* Deg. 


6<H Deg. 



29* 



()2 



TRAVERSE TABLE. 



j 

g 

3" 

o 


30 Deg. 


30i Deg. 


30i Deg. 


30} Deg. 


d 

ST 

s 

» 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


0.87 


0.50 


0.86 


0.50 


0.86 


0.51 


0.86 


0.51 


1 




2 


1.73 


1.00 


1.73 


1.01 


1.72 


1.02 


1.72 


1.02 


2 




3 


2.60 


1.50 


2.59 


1.51 


2.58 


1.52 


2.58 


1.53 


3 




4 


3.46 


2.00 


3.46 


2.02 


3.45 


2.03 


3.44 


2.05 


4 




5 


4.33 


2.50 


4.32 


2.52 


4.31 


2.54 


4.30 


2.56 


5 




6 


5.20 


3.00 


5.18 


3.02 


5.17 


3.05 


5.16 


3.07 


6 




7 


6.06 


3.50 


6.05 


3.53 


6.03 


3.55 


6.02 


3.58 


7 




8 


6.93 


4.00 


6.91 


4.03 


6.89 


4.06 


6.88 


4.09 


8 




9 


7.79 


4.50 


7.77 


4.53 


7.75 


4.57 


7.73 


4.60 


9 




10 


8.66 


5.00 


8.64 


5.04 


8.62 


5.08 


8.59 


5.11 


10 




11 


9.53 


5.50 


9.50 


5.54 


9.48 


5.58 


9.45 


5.62 


11 




12 


10.39 


6.00 


10.37 


6.05 


10.34 


6.09 


10.31 


6.14 


12 




13 


11.26 


6.50 


11.23 


6.55 


11.20 


6.60 


11.17 


6.65 


13 




14 


12.12 


7.00 


12.09 


7.05 


12.06 


7.11 


12.03 


7.16 


14 




15 


12.99 


7.50 


12.96 


7.56 


12.92 


7.61 


12.89 


7.67 


15 




16 


13.86 


8.00 


13.82 


8.06 


13.79 


8.12 


13.75 


8.18 


16 




17 


14.72 


8.50 


14.69 


8.56 


14.65 


8.63 


14.61 


8.69 


17 




18 


15.59 


9.00 


15.55 


9.07 


15.51 


9.14 


15.47 


9.20 


18 




19 


16.45 


9.50 


16.41 


9.57 


16.37 


9-64 


16.33 


9.71 


19 




20 


17.32 


10.00 


17.28 


10.08 


17.23 


10.15 


17.19 


10.23 


20 




21 


18.19 


10.50 


18.14 


10.58 


18.09 


10.66 


18.05 


10.74 


21 




22 


19.05 


11.00 


19.00 


11.08 


18.96 


11.17 


18.91 


11.25 


22 




23 


19.92 


11.50 


19.87 


11.59 


19.82 


11.67 


19.77 


11.76 


23 




24 


20.78 


12.00 


20.73 


12.09 


20.68 


12.18 


20.63 


12.27 


24 




25 


21.65 


12.50 


21.60 


12.59 


21.54 


12.69 


21.49 


12.78 


25 




26 


22.52 


13.00 


22.46 


13.10 


22.40 


13.20 


22.34 


13.29 


26 




27 


23.38 


13.50 


23.32 


13.60 


23.26 


13.70 


23.20 


13.80 


27 




28 


24.25 


14.00 


24.19 


14.11 


24.13 


14.21 


24.06 


14.32 


2fl 




29 


25.11 


14.50 


25.05 


14.61 


24.99 


14.72 


24.92 


14.83 


29 




30 


25.98 


15.00 


25.92 


15.11 


25.85 


15.23 


25.78 


15.34 


30 




31 


26.85 


15.50 


26.78 


15.62 


26.71 


15.73 


26.64 


15.85 


31 




32 


27.71 


16.00 


27.64 


16.12 


27.57 


16.24 


27.50 


16.36 


32 




33 


28.58 


16.50 


28.51 


16.62 


28.43 


16.75 


28.36 


16.87 


33 




34 


29.44 


17.00 


29.37 


17.13 


29.30 


17.26 


29.22 


17.38 


34 




35 


30.31 


17.50 


30.23 


17.63 


30.16 


17.76 


30.08 


17.90 


35 




36 


31.18 


18.00 


31.10 


18.14 


31.02 


18.27 


30.94 


18.41 


36 




37 


32.04 


18.50 


31.96 


18.64 


31.88 


18.78 


31.80 


18.92 


37 




38 


32.91 


19.00 


32.83 


19.14 


32.74 


19.29 


32.66 


19.43 


38 




39 


33.77 


19.50 


33.69 


19.65 


33.60 


19.79 


33.52 


19.94 


39 




40 


34.64 


20.00 


34.55 


20.15 


34.47 


20.30 


34.38 


20.45 


40 




41 


35.51 


20.50 


35.42 


20.65 


35.33 


20.81 


35.24 


20.96 


41 




42 


36.37 


21.00 


36.28 


21.16 


36.19 


21.32 


36.10 


21.47 


42 




43 


37.24 


21.50 


37.14 


21.66 


37.05 


21.82 


36.95 


21.99 


43 




44 


38.11 


22.00 


38.01 


22.17 


37.91 


22.33 


37.81 


22.50 


44 




45 


38.97 


22.50 


38.87 


22.67 


38.77 


22.84 


38.67 


23.01 


45 




46 


39.84 


23.00 


39.74 


23.17 


39.63 


23.35 


39.53 


23.52 


46 




47 


40.70 


23.50 


40.60 


23.68 


40.50 


23.85 


40.39 


24.03 


47 




48 


41.57 


24.00 


41.46 


24.18 


41.36 


24.36 


41.25 


24.54 


48 




49 


42.44 


24.50 


42.33 


24.68 


42.22 


24.87 


42.11 


25.05 


49 




50 


43.30 


25.00 


43.19 


25.19 


43.08 


25.38 


42.97 


25.56 


50 




a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 






60 1 


)eg. 


59J Deg. 


59$ 


Deg. 


59* 


Deg. 



TRAVERSE TABLE. 



03 



b 

B 

o 

(8 


30 Deg. 


30* Deg. 


30i Deg. 


30f Deg. 


B 

a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


44.17 


25.50 


44.06 


25.69 


43.94 


25.88 


43.83 


26.08 


51 


52 


45.03 


26.00 


44.92 


26.20 


44.80 


26.39 


44.69 


26.59 


52 


53 


45.90 


26.50 


45.78 


26.70 


45.67 


26.90 


45.55 


27.10 


53 


54 


46.77 


27.00 


46.65 


27.20 


46.53 


27.41 


46.41 


27.61 


54 


55 


47.63 


27.50 


47.51 


27.71 


47.39 


27.91 


47.27 


28.12 


55 


56 


48.50 


28.00 


48.37 


28.21 


48.25 


28.42 


48.13 


28.63 


56 


57 


49-36 


28.50 


49.24 


28.72 


49.11 


28.93 


48.99 


29.14 


57 


58 


50.23 


29.00 


50.10 


29.22 


49.97 


29.44 


49.85 


29.65 


58 


59 


51.10 


29.50 


50.97 


29.72 


50.84 


29.94 


50.70 


30.17 


59 


60 


51.96 


30.00 


51.83 


30.23 


51.70 


30.45 


51.56 


30.68 


60 


61 


52.83 


30.50 


52.69 


30.73 


52.56 


30.96 


52.42 


31.19 


61 


62 


53.69 


31.00 


53.56 


31.23 


53.42 


31.47 


53.28 


31.70 


62 


63 


54.56 


31.50 


54.42 


31.74 


54.28 


31.97 


54.14 


32.21 


63 


64 


55.43 


32.00 


55.29 


32.24 


55.14 


32.48 


55.00 


32.72 


64 


65 


56.29 


32.50 


56.15 


32.75 


56.01 


32.99 


55.86 


33.23 


65 


66 


57.16 


33.00 


57.01 


33.25 


56.87 


33.50 


56.72 


33.75 


66 


67 


58-02 


33.50 


57.88 


33.75 


57.73 


34.01 


57.58 


34.26 


67 


68 


58.89 


34.00 


58.74 


34.26 


58.59 


34.51 


58.44 


34.77 


68 


69 


59.76 


34.50 


59.60 


34.76 


59.45 


35.02 


59.30 


35.28 


69 


70 


60.62 


35.00 


60.47 


35.26 


60.31 


35.53 


60.16 


35.79 


70 


71 


61.49 


35.50 


61.33 


35.77 


61.18 


36.04 


61.02 


36.30 


71 


72 


62.35 


36.00 


62.20 


36.27 


62.04 


36.54 


61.88 


36.81 


72 


73 


63.22 


36.50 


63.06 


36.78 


62.90 


37.05 


62.74 


37.32 


73 


74 


64.09 


37.00 


63.92 


37.28 


63.76 


37.56 


63.60 


37.84 


74 


75 


64.95 


37.50 


64.79 


37.78 


64.62 


38.07 


64.46 


38.35 


75 


76 


65.82 


38.00 


65.65 


38.29 


65.48 


38.57 


65.31 


38.86 


76 


77 


66.68 


38.50 


66.52 


38.79 


66.35 


39.08 


66.17 


39.37 


77 


78 


67.55 


39.00 


67.38 


39.29 


67.21 


39.59 


67.03 


39.88 


78 


79 


68.42 


39.50 


68.24 


39.80 


68.07 


40.10 


67.89 


40.39 


79 


80 


69.28 


40.00 


69.11 


40.30 


68.93 


40.60 


68.75 


40.90 


80 


81 


70.15 


40.50 


69.97 


40.81 


69.79 


41.11 


69.61 


41.41 


81 


82 


71.01 


41.00 


70.83 


41.31 


70.65 


41.62 


70.47 


41.93 


82 


83 


71.88 


41.50 


71.70 


41.81 


71.52 


42.13 


71.33 


42.44 


83 


84 


72.75 


42.00 


72.56 


42.32 


72.38 


42.63 


72.19 


42.95 


84 


85 


73.61 


42.50 


73.43 


42.82 


73.24 


43.14 


73.05 


43.46 


85 


86 


74.48 


43.00 


74.29 


43.32 


74.10 


43.65 


73.91 


43.97 


86 


87 


75.34 


43.50 


75.15 


43.83 


74.96 


44.16 


74.77 


44.48 


87 


88 


76.21 


44.00 


76.02 


44.33 


75.82 


44.66 


75.63 


44.99 


88 


89 


77.08 


44.50 


76.88 


44.84 


76.68 


45.17 


76.49 


45.51 


89 


90 


77.94 


45.00 


77.75 


45.34 


77.55 


45.68 


77.35 


46.02 


90 


91 


78.81 


45.50 


78.61 


45.84 


78.41 


46.19 


78.21 


46.53 


91 


92 


79.67 


46.00 


79.47 


46.35 


79.27 


46.69 


79.07 


47.04 


92 


93 80.54 


46.50 


80.34 


46.85 


80.13 


47.20 


79.92 


47.55 


93 


94 


81.41 


47.00 


81.20 


47.35 


80.99 


47.71 


80.78 


48.06 


94 


95 


82.27 


47.50 


82.06 


47.86 


81.85 


48.22 


81.64 


48.57 


95 


96 


83.14 


48.00 


82.93 


48.36 


82.72 


48.72 


82.50 


49.08 


96 


97 


84.00 


48.50 


83.79 


48.87 


83.58 


49.23 


83.36 


49.60 


97 ; 


98 


84.87 


49.00 


84.66 


49.37 


84.44 


49.74 


84.22 


50.11 


98 


99 


85.74 


49.50 


85.52 


49.87 


85.30 


50.25 


85.08 


50.62 


99 


100 


86.60 


50.00 


86.38 


50.38 


86.16 


50.75 


85.94 


51.13 


100 

V 

o 
a 
rt 

Q 


a 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


60 1 


)eg. 


59| Deg. 


59h Deg. 


59} Deg. 



64 



TRAVERSE TABLE. 





o 
n 


31 Deg. 


3U Deg. 


31i Deg. 


31} Deg. 



F 

s 
n 
o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.86 


0.51 


0.85 


0.52 


0.85 


0.52 


0.85 


0.53 


1 


2 


1.71 


1.03 


1.71 


1.04 


1.71 


1.04 


1.70 


1.05 


2 


3 


2.57 


1.55 


2.56 


1.56 


2.56 


1.57 


2.55 


1.58 


3 


4 


3.43 


2.06 


3.42 


2.08 


3.41 


2.09 


3.40 


2.10 


4 


5 


4.29 


2.58 


4.27 


2.59 


4.26 


2.61 


4.25 


2.63 


5 


6 


5.14 


3.09 


5.13 


3.11 


5.12 


3.13 


5.10 


3.16 


6 


7 


6.00 


3.61 


5.98 


3.63 


5.97 


3.66 


5.95 


3.68 


7 


8 


6.86 


4.12 


6.84 


4.15 


6.82 


4.18 


6.80 


4.21 


8 


9 


7.71 


4.64 


7.69 


4.67 


7.67 


4.70 


7.65 


4.74 


9 


10 


8.57 


5.15 


8.55 


5.19 


8.53 


5.22 


8.50 


5.26 


10 


11 


9.43 


5.67 


9.40 


5.71 


9.38 


5.75 


9.35 


5.79 


11 


12 


10.29 


6.18 


10.26 


6.23 


10.23 


6.27 


10.20 


6.31 


12 


13 


11.14 


6.70 


11.11 


6.74 


11.08 


6.79 


11.05 


6.84 


13 


14 


12.00 


7.21 


11.97 


7.26 


11.94 


7.31 


11.90 


7.37 


14 


15 


12.86 


7.73 


12.82 


7.78 


12.79 


7.84 


12.76 


7.89 


15 


16 


13.71 


8.24 


13.68 


8.30 


13.64 


8.36 


13.61 


8.42 


16 


17 


14.57 


8.76 


14.53 


8.82 


14.49 


8.88 


14.46 


8.95 


17 


18 


15.43 


9.27 


15.39 


9.34 


15.35 


9.40 


15.31 


9.47 


18 


19 


16.29 


9.79 


16.24 


9.86 


16.20 


9.93 


16.16 


10.00 


19 : 


20 


17.14 


10.30 


17.10 


10.38 


17.05 


10.45 


17.01 


10.52 


20 


21 


18.00 


10.82 


17.95 


10.89 


17.91 


10.97 


17.86 


11.05 


21 


22 


18.86 


11.33 


18.81 


11.41 


18.76 


11.49 


18.71 


11.58 


22 


23 


19.71 


11.85 


19.66 


11.93 


19.61 


12.02 


19.56 


12.10 


23 


24 


20.57 


12.36 


20.52 


12.45 


20.46 


12.54 


20.41 


12.63 


24 


25 


21.43 


12.88 


21.37 


12.97 


21.32 


13.06 


21.26 


13.16 


25 


26 


22.29 


13.39 


22.23 


13.49 


22.17 


13.58 


22.11 


13.68 


26 


27 


23.14 


13.91 


23.08 


14.01 


23.02 


14.11 


22.96 


14.21 


27 


28 


24.00 


14.42 


23.94 


14.53 


23.87 


14.63 


23.81 


14.73 


28 


29 


24.86 


14.94 


24.79 


15.04 


24.73 


15.15 


24.66 


15.26 


29 


30 


25.71 


15.45 


25.65 


15.56 


25.58 


15.67 


25.51 


15.79 


30 


31 


26.57 


15.97 


26.50 


16.08 


26.43 


16.20 


26.36 


16.31 


31 


32 


27.43 


16.48 


27.36 


16.60 


27.28 


16.72 


27.21 


16.84 


32 


33 


28.29 


17.00 


28.21 


17.12 


28.14 


17.24 


28.06 


17.37 


33 


34 


29.14 


17.51 


29.07 


17.64 


28.99 


17.76 


28.91 


17.89 


34 


35 


30.00 


18.03 


29.92 


18.16 


29.84 


18.29 


29.76 


18.42 


35 


36 


30.86 


18.54 


30.78 


18.68 


30.70 


18.81 


30.61 


18.94 


36 


37 


31.72 


19.06 


31.63 


19.19 


31.55 


19.33 


31.46 


19.47 


37 


38 


32.57 


19.57 


32.49 


19.71 


32.40 


19.85 


32.31 


20.00 


38 


39 


33.43 


20.09 


33.34 


20.23 


33.25 


20.38 


33.16 


20.52 


39 


40 


34.29 


20.60 


34.20 


20.75 


34.11 


20.90 


34.01 


21.05 


40 


i 41 


35.14 


21.12 


35.05 


21.27 


34.96 


21.42 


34.86 


21.57 


41 


42 


36.00 


21.63 


35.91 


21.79 


35.81 


21.94 


35.71 


22.10 


42 


43 


36.86 


22.15 


36.76 


22.31 


36.66 


22.47 


36.57 


22.63 


43 


44 


37.72 


22.66 


37.62 


22.83 


37.52 


22.99 


37.42 


23.15 


44 


45 


38.57 


23.18 


33.47 


23.34 


38.37 


23.51 


38.27 


23.68 


45 


46 


39.43 


23.69 


39.33 


23.86 


39.22 


24.03 


39.12 


24.21 


46 


i 47 


40.29 


24.21 


40.18 


24.38 


40.07 


24.56 


39.97 


24.73 


47 


48 


41.14 


24.72 


41.04 


24.90 


40.93 


25.08 


40.82 


25.26 


48 


49 


42.00 


25.24 


41.89 


25.42 


41.78 


25.60 


41.67 


25.78 


49 


50 


42.86 


25.75 


42.75 


25.94 


42.63 


26.12 


42.52 


26.31 


50 


6 
a 

1 J 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. | Lat. 


i 


59 I 


)eg. 


58} 


Deg. 


58J] 


Deg. 


58* Deg. 


i 



TRAVERSE TABLE. 



65 



e 

a- 

1 

o 
a 

51 


31 Deg. 


31} Deg. 


31i Deg. 


31| Deg. 


£ 
o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


43.72 


26.27 


43.60 


26.46 


43.48 


26.65 


43.37 


26.84 


51 


52 


44.57 


26.78 


44.46 


26.98 


44.34 


27.17 


44.22 


27.36 


52 


53 


45.43 


27.30 


45.31 


27.49 


45.19 


27.69 


45.07 


27.89 


53 1 


54 


46.29 


27.81 


46.17 


28.01 


46.04 


28.21 


45.92 


28.42 


54 | 


55 


47.14 


28.33 


47.02 


28.53 


46.90 


28.74 


46.77 


28.94 


55 i 


56 


48.00 


28.84 


47.88 


29.05 


47.75 


29.26 


47.62 


29.47 


56 3 


57 


48.86 


29.36 


48.73 


29.57 


48.60 


29.78 


48.47 


2&.99 


57 | 


58 


49.72 


29.87 


49.58 


30.09 


49.45 


30.30 


49.32 


30.52 


58 i 


59 


50.57 


30.39 


50.44 


30.61 


50.31 


30.83 


50.17 


31.05 


59 | 


60 


51.43 


30.90 


51.29 


31.13 


51.16 


31.35 


51.02 


31.57 


60 J 


61 


52.29 


31.42 


52.15 


31.65 


52.01 


31.87 


51.87 


32.10 


61 1 


62 


53.14 


31.93 


53.00 


32.16 


52.86 


32.39 


52.72 


32.63 


62 S 


63 


54.00 


32.45 


53.86 


32.68 


53.72 


32.92 


53.57 


33.15 


63 | 


64 


54.86 


32.96 


54.71 


33.20 


54.57 


33.44 


54.42 


33.68 


64 


65 


55.72 


33.48 


55.57 


33.72 


55.42 


33.96 


55.27 


34.20 


65 


66 


56.57 


33.99 


56.42 


34.24 


56.27 


34.48 


56.12 


34.73 


66 


67 


57.43 


34.51 


57.28 


34.76 


57.13 


35.01 


56.98 


35.26 


67 


68 


58.29 


35.02 


58.13 


35.28 


57.98 


35.53 


57.82 


35.78 


68 


69 


59.14 


35.54 


58.99 


35.80 


58.83 


36.05 


58.67 


36.31 


69 


70 


60.00 


36.05 


59.84 


36.31 


59.68 


36.57 


59.52 


36.83 


70 


71 


60.86 


36.57 


60.70 


36.83 


60.54 


37.10 


60.37 


37.36 


71 


72 


61.72 


37.08 


61.55 


37.35 


61.39 


37.62 


61.23 


37.89 


72 


73 


62.57 


37.60 


62.41 


37.87 


62.24 


38.14 


62.08 


38.41 


73 


74 


63.43 


38.11 


63.26 


38.39 


63.10 


38.66 


62.93 


38.94 


74 


75 


64.29 


38.63 


64.12 


38.91 


63.95 


39.19 


63.78 


39.47 


75 


76 


65.14 


39.14 


64.97 


39.43 


64.80 


39.71 


64.63 


39.99 


76 


77 


66.00 


39.66 


65.83 


39.95 


65.65 


40.23 


65.48 


40.52 


77 


78 


66.86 


40.17 


66.68 


40.46 


66.51 


40.75 


66.33 


41.04 


78 


79 


67.72 


40.69 


67.54 


40.98 


67.36 


41.28 


67.18 


41.57 


79 


80 


68.57 


41.20 


68.39 


41.50 


68.21 


41.80 


68.03 


42.10 


80 


81 


69.43 


41.72 


69.25 


42.02 


69.06 


42.32 


68.88 


42.62 


81 


82 


70.29 


42.23 


70.10 


42.54 


69.92 


42.84 


69.73 


43.15 


82 


83 


71.14 


42.75 


70.96 


43.06 


70.77 


43.37 


70.58 


43.68 


83 


84 


72.00 


43.26 


71.81 


43.58 


71.62 


43.89 


71.43 


44.20 


84 


85 


72.86 


43.78 


72.67 


44.10 


72.47 


44.41 


72.28 


44.73 


85 


86 


73.72 


44.29 


73.52 


44.61 


73.33 


44.93 


73.13 


45.25 


86 


87 


74.57 


44.81 


74.38 


45.13 


74.18 


45.46 


73.98 


45.78 


87 


88 


75.43 


45.32 


75.23 


45.65 


75.03 


45.98 


74.83 


46.31 


88 


89 


76.29 


45.84 


76.09 


46.17 


75.88 


46.50 


75.68 


46.83 


89 


90 


77.15 


46.35 


76.94 


46.69 


76.74 


47.02 


76.53 


47.36 


90 


91 


78.00 


46.87 


77.80 


47.21 


77.59 


47.55 


77.38 


47.89 


91 


92 


78.86 


47.38 


78.65 


47.73 


78.44 


48.07 


78.23 


48.41 


92 


93 


79.72 


47.90 


79.51 


48.25 


79.30 


48.59 


79.08 


48.94 


93 


94 


80.57 


48.41 


80.36 


48.76 


80.15 


49.11 


79.93 


49.47 


94 


95 


81.43 


48.93 


81.22 


49.28 


81.00 


49.64 


80.78 


49.99 


95 


96 


82.29 


49.44 


82.07 


49.80 


81.85 


50.16 


81.63 


50.52 


96 


97 


83.15 


49.96 


82.93 


50.32 


82.71 


50.68 


82.48 


51.04 


97 


98 


84.00 


50.47 


83.78 


50.84 


83.56 


51.20 


83.33 


51.57 


98 


99 


84.86 


50.99 


84.64 


51.36 


84.41 


51.73 


84.18 


52.10 


99 


100 


85.72 


51.50 


85.49 


51.88 


85.26 


52.25 


85.04 


52.62 


100 


Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 
a 

Q 


59 ] 


Deg. 


58| 


Deg. 

1 


58i 


Deg. 


58* 


Deg. 



2X 



06 



TRAVERSE TABLE. 



g 
1 

a 


32 Deg. 


32} Deg. 


32* Deg. 


32* Deg. 


a 

3 
O 

5 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.85 


0.53 


0.85 


0.53 


0.84 


0.54 


0.84 


0.54 


1 


2 


1.70 


1.06 


1.69 


1.07 


1.69 


1.07 


1.68 


1.08 


2 


3 


2.54 


1.59 


2.54 


1.60 


2.53 


1.61 


2.52 


1.62 


3 


4 


3.39 


2.12 


3.38 


2.13 


3.37 


2.15 


3.36 


2.16 


4 


5 


4.24 


2.65 


4.23 


2.67 


4.22 


2.69 


4.21 


2.70 


5 


6 


5.09 


3.18 


5.07 


3.20 


5.06 


3.22 


5.05 


3.25 


3 


7 


5.94 


3.71 


5.92 


3.74 


5.90 


3.76 


5.89 


3 79 


7 


8 


6.78 


4.24 


6.77 


4.27 


6.75 


4.30 


6.73 


4.33 


8 


9 


7.63 


4.77 


7.61 


4.80 


7.59 


4.84 


7.57 


4.87 


9 


10 


8.48 


5.30 


8.46 


5.34 


8.43 


5.37 


8.41 


5.41 


10 


11 


9.33 


5.83 


9.30 


5.87 


9.28 


5.91 


9.25 


5.95 


11 


12 


10.18 


6.36 


10.15 


6.40 


10.12 


6.45 


10.09 


6.49 


12 


13 


11.02 


6.89 


10.99 


6.94 


10.96 


6.98 


10.93 


7.03 


13 


14 


11.87 


7.42 


11.84 


7.47 


11.81 


7.52 


11.77 


7.57 


14 


15 


12.72 


7.95 


12.69 


8.00 


12.65 


8.06 


12.62 


8.11 


15 


16 


13.57 


8.48 


13.53 


8.54 


13.49 


8.60 


13.46 


8.66 


16 


17 


14.42 


9.01 


14.38 


9.07 


14.34 


9.13 


14.30 


9.20 


17 


18 


15.26 


9.54 


15.22 


9.61 


15.18 


9.67 


15.14 


9.74 


18 


19 


16.11 


10.07 


16.07 


10.14 


16.02 


10.21 


15.98 


10.28 


19 


20 


16.96 


10.60 


16.91 


10.67 


16.87 


10.75 


16.82 


10.82 


20 


21 


17.81 


11.13 


17.76 


11.21 


17.71 


11.28 


17.66 


11.36 


21 


22 


18.66 


11.66 


18.61 


11.74 


18.55 


11.82 


18.50 


11.90 


22 


23 


19.51 


12.19 


19.45 


12.27 


19.40 


12.36 


19.34 


12.44 


23 


24 


20.35 


12.72 


20.30 


12.81 


20.24 


12.90 


20.18 


12.98 


24 


25 


21.20 


13.25 


21.14 


13.34 


21.08 


13.43 


21.03 


13.52 


25 


26 


22.05 


13.78 


21.99 


13.87 


21.93 


13.97 


21.87 


14.07 


26 


27 


22.90 


14.31 


22.83 


14.41 


22.77 


14.51 


22.71 


14.61 


27 


28 


23.75 


14.84 


23.68 


14.94 


23.61 


15.04 


23.55 


15.15 


28 


29 


24.59 


15.37 


24.53 


15.47 


24.46 


15.58 


24.39 


15.69 


29 


30 


25.44 


15.90 


25.37 


16.01 


25.30 


16.12 


25.23 


16.23 


30 


31 


26.29 


16.43 


26.22 


16.54 


26.15 


16.66 


26.07 


16.77 


31 


32 


27.14 


16.96 


27.06 


17.08 


26.99 


17.19 


1 26.91 


17.31 


32 


33 


27.99 


17.49 


27.91 


17.61 


27.83 


17.73 


27.75 


17.85 


33 


34 


28.83 


18.02 


28.75 


18.14 


28.68 


18.27 


28.60 


18.39 


34 


35 


29.68 


18.55 


29.60 


18.68 


29.52 


18.81 


29.44 


18.93 


35 


36 


30.53 


19.08 


30.45 


19.21 


30.36 


19.34 


30.28 


19.48 


36 


37 


31.38 


19.61 


31.29 


19.74 


31.21 


19.88 


31.12 


20.02 ! 37 


38 


32.23 


20.14 


32.14 


20.28 


32.05 


20.42 


31.96 


20.56 | 38 


39 


33.07 


20.67 


32.98 


20.81 


32.89 


20.95 


32.80 


21.10 39 


40 


33.92 


21.20 


33.83 


21.34 


33.74 


21.49 


33.64 


21.64 40 


41 


34.77 


21.73 


34.67 


21.88 


34.58 


22.03 


34.48 


22.18 


41 


42 


35.62 


22.26 


35.52 


22.41 


35.42 


22.57 


35.32 


22.72 


42 


43 


36.47 


22.79 


36.37 


22.95 


36.27 


23.10 


36.16 


23.26 


43 


44 


37.31 


23.32 


37.21 


23.48 


37.11 


23.64 


37.01 


23.80 


44 


45 


38.16 


23.85 


38.06 


24.01 


37.95 


24.18 


37.85 


24.34 


45 


46 


39.01 


24.38 


38.90 


24.55 


38.80 


24.72 


38.69 


24.88 


46 


47 


39.86 


24.91 


39.75 


25.08 


39.64 


25.25 


39.53 


25.43 


47 


48 


40.71 


25.44 


40.59 


25.61 


40.48 


25.79 


40.37 


25.97 


4!! 


49 


41.55 


25.97 


41.44 


26.15 


41.33 


26.33 


41.21 


26.51 


49 \ 


50 


42.40 


26.50 


42.29 


26.68 


42.17 


26.86 


42.05 


27.05 


50 


e 
.2 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


<u 


58 ] 


)eg. 


57J 


Deg. 


57* Deg. 


57} 


Deg. 


s 



TRAVERSE TABLE. 



67 



g 

s 
? 


32 Deg. 


32* Deg. 


32* Deg. 


32J Deg. 


e 

1 
a 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


43.25 


27.03 


43.13 


27.21 


43.01 


27.40 


42.89 


27.59 


51 


52 


44.10 


27.56 


43.98 


27.75 


43.86 


27.94 


43.73 


28.13 


52 


53 


44.95 


28.09 


44.82 


28.28 


44.70 


28.48 


44.58 


28.67 


53 


54 


45.79 


28.62 


45.67 


28.82 


45.54 


29.01 


45.42 


29.21 


54 


55 


46.64 


29.15 


46.51 


29.35 


46.39 


29.55 


46.26 


29.75 


55 


56 


47.49 


29.68 


47.36 


29.88 


47.23 


30.09 


47.10 


30.29 


56 


57 


48.34 


30.21 


48.21 


30.42 


48.07 


30.63 


47,94 


30.84 


57 


58 


49.19 


30.74 


49.05 


30.95 


48.92 


31.16 


48.78 


31.38 


58 


59 


50.03 


31.27 


49.90 


31.48 


49.76 


31.70 


49.62 


31.92 


59 


60 


50.88 


31.80 


50.74 


32.02 


50.60 


32.24 


50.46 


32.46 


60 


61 


51.73 


32.33 


51.59 


32.55 


51.45 


32.78 


51.30 


33.00 61 


62 


52.58 


32.85 


52.44 


33.08 


52.29 


33.31 


52.14 


33.54 


62 


63 


53.43 


33.38 


53.28 


33.62 


53.13 


33.85 


52.99 


34.08 


63 


64 


54.28 


33.91 


54.13 


34.15 


53.98 


34.39 


53.83 


34.62 


64 


65 


55.12 


34.44 


54.97 


34.68 


54.82 


34.92 


54.67 


35.16 


65 


66 


55.97 


34.97 


55.82 


35.22 


55.66 


35.46 


55.51 


35.70 


66 


67 


56.82 


35.50 


56.66 


35.75 


56.51 


36.00 


56.35 


36.25 


67 


68 


57.67 


36.03 


57.51 


36.29 


57.35 


36.54 


57.19 


36.79 


68 


69 


58.52 


36.56 


58.36 


36.82 


58.19 


37.07 


58.03 


37.33 


69 


70 


59.36 


37.09 


59.20 


37.35 


59.04 


37.61 


58.87 


37.87 


70 


71 


60.21 


37.62 


60.05 


37.89 


59.88 


38.15 


59.71 


38.41 


71 


72 


61.06 


38.15 


60.89 


38.42 


60.72 


38.69 


60.55 


38.95 


72 


73 


61.91 


38.68 


61.74 


38.95 


61.57 


39.22 


61.40 


39.49 


73 


74 


62.76 


39.21 


62.58 


39.49 


62.41 


39.76 


62.24 


40.03 


74 


75 


63.60 


39.74 


63.43 


40.02 


63.25 


40.30 


63.08 


40.57 


75 


76 


64.45 


40.27 


64.28 


40.55 


64.10 


40.83 


63.92 


41.11 


76 


77 


65.30 


40.80 


65.12 


41.09 


64.94 


41.37 


64.76 


41.65 


77 


78 


66.15 


41.33 


65.97 


41.62 


65.78 


41.91 


65.60 


42.20 


78 


79 


67.00 


41.86 


66.81 


42.16 


66.63 


42.45 


66.44 


42.74 


79 


80 


67.84 


42.39 


67.66 


42.69 


67.47 


42.98 


67.28 


43.28 


80 


81 


68.69 


42.92 


68.50 


43.22 


68.31 


43.52 


68.12 


43.82 


81 


82 


69.54 


43.45 


69.35 


43.76 


69.16 


44.06 


68.97 


44.36 


82 


83 


70.39 


43.98 


70.20 


44.29 


70.00 


44.60 


69.81 


44.90 


83 


84 


71.24 


44.51 


71.04 


44.82 


70.84 


45.13 


70.65 


45.44 


84 


85 


72.08 


45.04 


71.89 


45.36 


71.69 


45.67 


71.49 


45.98 


85 


86 


72.93 


45.57 


72.73 


45.89 


72.53 


46.21 


72.33 


46.52 


86 


87 


73.78 


46.10 


73.58 


46.42 


73.38 


46.75 


73.17 


47.06 


87 


88 


74.63 


46.63 


74.42 


46.96 


74.22 


47.28 


74.01 


47.61 


88 


89 


75.48 


47.16 


75.27 


47.49 


75.06 


47.82 


74.85 


48.15 


89 


90 


76.32 


47.69 


76.12 


48.03 


75.91 


48.36 


75.69 


48.69 


90 


91 


77.17 


48.22 


76.96 


48.56 


76.75 


48.89 


76.53 


49.23 


91 


92 


78.02 


48.75 


77.81 


49.09 


77.59 


49.43 


77.38 


49.77 


92 


93 


78.87 


49.28 


78.65 


49.63 


78.44 


49.97 


78.22 


50.31 


93 


94 


79.72 


49.81 


79.50 


50.16 


79.28 


50.51 


79.06 


50.85 


94 


95 


80.56 


50.34 


80.34 


50.69 


80.12 


51.04 


79.90 


51.39 


95 


96 


81.41 


50.87 


81.19 


51.23 


80.97 


51.58 


80.74 


51.93 


96 


97 


82.26 


51.40 


82.04 


51.76 


81.81 


52.12 


81.58 


52.47 


97 


98 


83.11 


51.93 


82.88 


52.29 


82.65 


52.66 


82.42 


53.02 


98 


99 


83.96 


52.46 


83.73 


52.83 


83.50 


53.19 


83.26 


53.56 


99 


100 


84.80 


52.99 : 


84.57 


53.36 


84.34 


53.73 


84.10 


54.10 


100 


1 
Q 


Dep. 


Lat. ! 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

a 
a 

5 


58 Deg. 


57* Deg. 


57£ Deg. 


57i Deg. 



63 



TRAVERSE TABLE. 




I 


33 Deg. 


33} Deg. 


33* Deo;. 


331 Deg. 


g 

ST 

3 

5 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


0.84 


0.54 


0.84 


0.55 


0.83 


0.55 


0.83 


0.56 


1 




2 1.68 


1.09 


1.67 


1.10 


1.67 


1.10 


1.66 


1.11 


2 




3 2.52 


1.63 


2.51 


1.64 


2.50 


1.66 


2.49 


1.67 


3 




4 


3.35 


2.18 


3.35 


2.19 


3.34 


2.21 


3.33 


2.22 


4 




5 


4.19 


2.72 


4.18 


2.74 


4.17 


2.76 


4.16 


2.78 


5 




6 


5.03 


3.27 


5.02 


3.29 


5.00 


3 31 


4.99 


3.33 


6 




7 


5.87 


3.81 


5.85 


3.84 


5.84 


3.86 


5.82 


3.89 


7 




8 


6.71 


4.36 


6.69 


4.39 


6.67 


4.42 


6.65 


4.44 


8 




9 


7.55 


4.90 


7.53 


4.93 


7.50 


4.97 


7.48 


5.00 


9 




10 


8.39 


5.45 


8.36 


5.48 


8.34 


5.52 


8.31 


5.56 


10 




11 


9.23 


5.99 


9.20 


6.03 


9.17 


6.07 


9.15 


6.11 


11 




12 


10.06 


6.54 


10.04 


6.58 


10.01 


6.62 


9.98 


6.67 


12 




13 


10.90 


7.08 


10.87 


7.13 


10.84 


7.18 


10.81 


7.22 


13 




14 


11.74 


7.62 


11.71 


7.68 


11.67 


7.73 


11.64 


7.78 


14 




15 


12.58 


8.17 


12.54 


8.22 


12.51 


8.28 


12.47 


8.33 


15 




16 


13.42 


8.71 


13.38 


8.77 


13.34 


8.83 


13.30 


8.89 


16 




17 


14.26 


9.26 


14.22 


9.32 


14.18 


9.38 


14.13 


9.44 


17 




18 


15.10 


9.80 


15.05 


9.87 


15.01 


9.93 


14.97 


10.00 


18 




19 


15.93 


10.35 


15.89 


10.42 


15.84 


10.49 


15.80 


10.56 


19 




20 


16.77 


10.89 


16.73 


10.97 


16.68 


11.04 


16.63 


11.11 


20 




21 


17.61 


11.44 


17.56 


11.51 


17.51 


11.59 


17.46 


11.67 


21 




22 


18.45 


11.98 


18.40 


12.06 


18.35 


12.14 


18.29 


12.22 


22 




23 


19.29 


12.53 


19.23 


12.61 


19.18 


12.69 


19.12 


12.78 


23 




24 


20.13 


13.07 


20.07 


13.16 


20.01 


13.25 


19.96 


13.33 


24 




25 


20.97 


13.62 


20.91 


13.71 


20.85 


13.80 


20.79 


13.89 


25 




26 


21.81 


14.16 


21.74 


14.26 


21.68 


14.35 


21.62 


14.44 


26 




27 


22.64 


14.71 


22.58 


14.80 


22.51 


14.90 


22.45 


15.00 


27 




28 


23.48 


15.25 


23.42 


15.35 


23.35 


15.45 


23.28 


15.56 


28 




29 


24.32 


15.79 


24.25 


15. Q0 


24.18 


16.01 


24.11 


16.11 


29 




30 


25.16 


16.34 


25.09 


16.45 


25.02 


16.56 


24.94 


16.67 


30 




31 


26.00 


16.88 


25.92 


17.00 


25.85 


17.11 


25.78 


17.2-2 


31 




32 


26.84 


17.43 


26.76 


17.55 


26.68 


17.66 


26.61 


17.78 


32 




33 


27.68 


17.97 


27.60 


18.09 


27.52 


18.21 


27.44 


18.33 


33 




34 


28.51 


18.52 


28.43 


18.64 


28.35 


18.77 


28.27 


18.89 


34 




35 


29.35 


19.06 


29.27 


19.19 


29.19 


19.32 


29.10 


19.44 


35 




36 


30.19 


19.61 


30.11 


19.74 


30.02 


19.87 


29.93 


20.00 


36 




37 


31.03 


20.15 


30.94 


20.29 


30.85 


20.42 


30.76 


20.56 


37 




38 


31.87 


20.70 


31.78 


20.84 


31.69 


20.97 


31.60 


21.11 


38 




39 


32.71 


21.24 


32.62 


21.38 


32.52 


21.53 


32.43 


21.67 


39 




40 


33.55 


21.79 


33.45 


21.93 


33.36 


22.08 


33.26 


22.22 


40 




41 


34.39 


22.33 


34.29 


22.48 


34.19 


22.63 


34.09 


22.78 


41 




42 


35.22 


22.87 


35.12 


23.03 


35.02 


23.18 


34.92 


23.33 


42 




43 


36.06 


23.42 


35.96 


23.58 


35.86 


23.73 


35.75 


23.89 


43 




44 


36.90 


23.96 


36.80 


24.12 


36.69 


24.29 


36.58 


24.45 


44 




45 


37.74 


24.51 


37.63 


24.67 


37.52 


24.84 


37.42 


25.00 


45 




46 


38.58 


25.05 


38.47 


25.22 


38.36 


25.39 


38.25 


25-56 


46 




47 


39.42 


25.60 


39.31 


25.77 


39.19 


25.94 


39.08 


26.11 


47 




48 


40.26 


26.14 


40.14 


26.32 


40.03 


26.49 


39.91 


26.67 


48 




49 


41.09 


26.69 


40.98 


26.87 


40.86 


27.04 


40.74 


27.22 


49 




50 


41.93 


27.23 


41.81 


27.41 


41.69 


27.60 


41.57 


27.78 


50 




l 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. 


Dep. 


Lat. 


s 
3 




57 I 


)eg. 


56| Deg. 


56i Deg. 1 


66i Deg. 





TRAVERSE TABLE. 



69 



? 


33 Deg. 


33i Deg. 


33i Deg. 


33| Deg. 


g 

1 
o 

CD 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


42.77 


27.78 


42.65 


27.96 


42.53 


28.15 


42.40 


28.33 


51 


52 


43.61 


28.32 


43.49 


28.51 


43.36 


28.70 


43.24 


28.89 


52 


53 


44.45 


28.87 


44.32 


29.06 


44.20 


29.25 


44.07 


29.45 


53 


54 


45.29 


29.41 


45.16 


29.61 


45.03 


29.80 


44.90 


30.00 


54 


55 


46.13' 


29.96 


46.00 


30.16 


45.86 


30.36 


45.73 


30.56 


55 


56 


46.97 


30.50 


46.83 


30.70 


46.70 


30.91 


46.56 


31.11 


56 


57 


47.80 


31.04 


47.67 


31.25 


47.53 


31.46 


47.39 


31.67 


57 


58 


48.64 


31.59 


48.50 


31.80 


48.37 


32.01 


48.23 


32.22 


58 


59 


49.48 


32.13 


49.34 


32.35 


49.20 


32.56 


49.06 


32.78 


59 


60 


50.32 


32.68 


50.18 


32.90 


50.03 


33.12 


49.89 


33.33 


60 


61 


51.16 


33.22 


51.01 


33.45 


50.87 


33.67 


50.72 


33.89 


61 


62 


52.00 


33.77 


51.85 


33.99 


51.70 


34.22 


51.55 


34.45 


62 


63 


52.84 


34.31 


52.69 


34.54 


52.53 


34.77 


52.38 


35.00 


63 


64 


53.67 


34.86 


53.52 


35.09 


53.37 


35.32 


53.21 


35.56 


64 


65 


54.51 


35.40 


54.36 


35.64 


54.20 


35.88 


54.05 


36.11 


65 


66 


55.35 


35.95 


55.19 


36.19 


55.04 


36.43 


54.88 


36.67 


66 


67 


56.19 


36.49 


56.03 


36.74 


55.87 


36.98 


55.71 


37.22 


67 


68 


57.03 


37.04 


56.87 


37.28 


56.70 


37.53 


56.54 


37.78 


68 


69 


57.87 


37.58 


57.70 


37.83 


57.54 


38.08 


57.37 


38.33 


69 i 


70 


58.71 


38.12 


58.54 


38.38 


58.37 


38.64 


58.20 


38.89 


70 


71 


59.55 


38.67 


59.38 


38.93 


59.21 


39.19 


59.03 


39.45 


71 


72 


60.38 


39.21 


60.21 


39.48 


60.04 


39.74 


59.87 


40.00 


72 


73 


61.22 


39.76 


61.05 


40.03 


60.87 


40.29 


60.70 


40.56 


73 


74 


62.06 


40.30 


61.89 


40.57 


61.71 


40.84 


61.53 


41.11 


74 


75 


62.90 


40.85 


62.72 


41.12 


62.54 


41.40 


62.36 


41.67 


75 


76 


63.74 


41.39 


63.56 


41.67 


63.38 


41.95 


63.19 


42.22 


76 


77 


64.58 


41.94 


64.39 


42.22 


64.21 


42.50 


64.02 


42.78 


77 


78 


65.42 


42.48 


65.23 


42.77 


65.04 


43.05 


64.85 


43.33 


78 


79 


66.25 


43.03 


66.07 


43.32 


65.88 


43.60 


65.69 


43.89 


79 


80 


67.09 


43.57 


66.90 


43. 86 


66.71 


44.15 


66.52 


44.45 


80 


81 


67.93 


44.12 


67.74 


44.41 


67.54 


44.71 


67.35 


45.00 


81 


82 


68.77 


44.66 


68.58 


44.96 


68.38 


45.28 


68.18 


45.56 


82 


83 


69.61 


45.20 


69.41 


45.51 


69.21 


45.81 


69.01 


46.11 


83 


84 


70.45 


45.75 


70.25 


46.06 


70.05 


46.36 


69.84 


46.67 


84 


85 


71.29 


46.29 


71.08 


46.60 


70.88 


46.91 


70.67 


47.22 


85 


86 


72.13 


46.84 


71.92 


47.15 


71.71 


47.47 


71.51 


47.78 


86 


! 87 


72.96 


47.38 


72.76 


47.70 


72.55 


48.02 


72.34 


48.33 


87 


88 


73.80 


47.93 


73.59 


48.25 


73.38 


48.57 


73.17 


48.89 


88 


89 


74.64 


48.47 


74.43 


48.80 


74.22 


49.12 


74.00 


49.45 


89 


90 


75.48 


49.02 


75.27 


49.35 


75.05 


49.67 


74.83 


50.00 


90 


91 


76.32 


49.56 


76.10 


49.89 


75.88 


50.23 


75.66 


50.56 


91 


92 


77.16 


50.11 


76.94 


50.44 


76.72 


50.78 


76.50 


51-11 


92 


93 


78.00 


50.65 


77.77 


50.99 


77.55 


51.33 


77.33 


51.67 


93 


94 


78.83 


51.20 


78.61 


51.54 


78.39 


51.88 


78.16 


52.22 


94 


95 


79.67 


51.74 


79.45 


52.09 


79.22 


52.43 


78.99 


52.78 


95 


96 


80.51 


52.29 


80.28 


52.64 


80.05 


52.99 


79.82 


53.33 


96 


97 


81.35 


52.83 


81.12 


53.18 


80.89 


53.54 


80.65 


53.89 


97 


98 


82.19 


53.37 


81.96 


53.73 


81.72 


54.09 


81.48 


54.45 


98 


99 


83.03 


53.92 


82.79 


54.28 


82.55 


54.64 


82.32 


55.00 


99 


100 


83.87 


54.46 


83.63 


54.83 


83.39 


55.19 


83.15 


55.56 


100 


a 
o 


Dep. 


Lat. 


Dep. 


Lat. i 


Dep. 


Lat. | 


Dep. 


Lat. 


«J 


57 Deg. 


I 
56| Deg. 


56$ Deg. 


563 Deg. 


i *~* 




1 


I 


" ! 



30 



70 



TRAVERSE TABLE, 



a 

a 
o 
? 


34 Deg. 


34* Deg. 


34* Deg. 


34* Deg. 


a 

a 
o 
? 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.83 


0.56 


0.83 


0.56 


0.82 


0.57 


0.82 


0.57 


1 


2 


1.66 


1.12 


1.65 


1.13 


1.65 


1.13 


1.64 


1.14 


2 


3 


2.49 


1.68 


2.48 


1.69 


2.47 


1.70 


2.46 


1.71 


3 


4 


3.32 


2.24 


3.31 


2.25 


3.30 


2.27 


3.29 


2.28 


4 


5 


4.15 


2.80 


4.13 


2.81 


4.12 


2.83 


4.11 


5.85 


5 


6 


4.97 


3.36 


4.96 


3.38 


4.94 


3.40 


4.93 


3.42 


6 


7 


5.80 


3.91 


5.79 


3.94 


5.77 


3.96 


5.75 


3.99 


7 


8 


6.63 


4.47 


6.61 


4.50 


6.59 


4.53 


6.57 


4.56 


8 


9 


7.46 


5.03 


7.44 


5.07 


7.42 


5.10 


7.39 


5.13 


9 


10 


8.29 


5.59 


8.27 


5.63 


8.24 


5.66 


8.22 


5.70 


10 


11 


9.12 


6.15 


9.09 


6.19 


9.07 


6.23 


9.04 


6.27 


11 


12 


9.95 


6-71 


9.92 


6.75 


9.89 


6.80 


9.86 


6.84 


12 


13 


10.78 


7.27 


10.75 


7.32 


10.71 


7.36 


10.68 


7.41 


13 


14 


11.61 


7.83 


11.57 


7.88 


11.54 


7.93 


11.50 


7.98 


14 


15 


12.44 


8.39 


12.40 


8.44 


12.36 


8.50 


12.32 


8.55 


15 


16 


13.26 


8-95 


13.23 


9.00 


13.19 


9.06 


13 15 


9.12 


16 


17 


14.09 


9.51 


14.05 


9.57 


14.01 


9.63 


13.97 


9.69 


17 


18 


14,92 


10.07 


14.88 


10-13 


14.83 


10.20 


14.79 


10.26 


18 


19 


15.75 


10.62 


15.71 


10-69 


15.66 


10.76 


15.61 


10.83 


19 


20 


16.58 


11.18 


16.53 


11.26 


16.48 


11.33 


16.43 


11.40 


20 


21 


17.41 


11.74 


17.36 


11.82 


17.31 


11.89 


17.25 


11.97 


21 


22 


18.24 


12.30 


18.18 


12.38 


18.13 


12.46 


18.08 


12.54 


22 


23 


19.07 


12.86 


19.01 


12.94 


18.95 


13.03 


18.90 


13.11 


23 


24 


19.90 


13.42 


19.84 


13.51 


19.78 


13.59 


19.72 


13.68 


24 


25 


20.73 


1-3.98 


20.66 


14-07 


20.60 


14.16 


20.54 


14.25 


25 


26 


21-55 


14.54 


21.49 


14-63 


21.43 


14.73 


21.36 


14.82 


26 


27 


22.38 


15.10 


22.32 


15.20 


22.25 


15.29 


22.18 


15.39 


27 


28 


23.21 


15.66 


23.14 


15.76 


23.08 


15.86 


23.01 


15.96 


28 


29 


24.04 


16.22 


23.97 


16.32 


23.90 


16.43 


23.83 


16.53 


29 


30 


24.87 


16.78 


24.80 


16.88 


24.72 


16-99 


24.65 


17.10 


30 


31 


25.70 


17.33 


25.62 


17-45 


25.55 


17.56 


25.47 


17.67 


31 


32 


26.53 


17,89 


26.45 


18.01 


26.37 


18.12 


26.29 


18.24 


32 


33 


27.36 


18,45 


27.28 


18.57 


27.20 


18.69 


27.11 


18.81 


33 


34 


23.19 


19.01 


28-10 


19.14 


28.02 


19.26 


27.94 


19.38 


34 


35 


29.02 


19-57 


28.93 


19.70 


28.84 


19.82 


28.76 


19.95 


35 


36 


29,85 


20.13 


29.76 


20.26 


29.67 


20.39 


29.58 


20.52 


36 


37 


30.67 


20.69 


30.58 


20.82 


30.49 


20.96 


30.40 


21.09 


37 


38 


31.50 


21.25 


31.41 


21.39 


31.32 


21.52 


31.22 


21.66 


38 


39 


32.33 


21.81 


32.24 


21.95 


32.14 


22.09 


32.04 


22.23 


39 


40 


33.16 


22.37 


33.06 


22.51 


32.97 


22.66 


32.87 


22.80 


40 


41 


33.99 


22.93 


33.89 


23.07 


33.79 


23.22 


33.69 


23.37 


41 


42 


34.82 


23.49 


34.72 


23.64 


34.61 


23.79 


34.51 


23.94 


42 


43 


35,65 


24.05 


35.54 


24.20 


35.44 


24.36 


35.33 


24.51 


43 


44 


36.48 


24.60 


36.37 


24.76 


36.26 


24.92 


36.15 


25.08 


44 


45 


37.31 


25.16 


37.20 


25.33 


37.09 


25.49 


36.97 


25.65 45 


46 


38.14 


25.72 


38.02 


25.89 


37.91 


26.05 


37.80 


26.22 


46 


47 


38.96 


26.28 


38.85 


26.45 


38.73 


26.62 


38.62 


26.79 


47 


48 


39.79 


26.84 


39.68 


27.01 


39.56 


27.19 


39.44 


27.36 


48 


49 


40.62 


27.40 


40.50 


27.58 


40.38 


27.75 


40.26 


27.93 


49 


50 


41.45 


27.96 


41.33 


28.14 


41.21 


28.32 


41.08 


28.50 


50 


o 

a 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 
1 

5 


56 ] 


)eg. 


55J Deg. 


55* Deg. 


55* Deg. 



TRAVERSE TABLE 



7] 



o 

B 
a 
? 


34 Deg. 


34* Deg. 


34i Deg. 


34| Deg. 


g 

S 
o 

Q 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


42.28 


28.52 


42.16 


28.70 


42.03 


28.89 


41.90 


29.07 


51 


52 


43.11 


29.08 


42.98 


29.27 


42.85 


29.45 


42.73 


29.64 


52 


53 


43.94 


29.64 


43.81 


29.83 


43.68 


30.02 


43.55 


30.21 


53 


54 


44.77 


30.20 


44.64 


30.39 


44.50 


30.59 


44.37 


30.78 


54 


55 


45.60 


30.76 


45.46 


30.95 


45.33 


31.15 


45.19 


31.35 


55 


56 


46.43 


31.31 


46.29 


31.52 


46.15 


31.72 


46.01 


31.92 


56 


57 


47.26 


31.87 


47.12 


32.08 


46.98 


32.29 


46.83 


32.49 


57 


58 


48.08 


32.43 


47.94 


32.64 


47.80 


32.85 


47.66 


33.06 


58 


59 


48.91 


32.99 


48.77 


33.21 


48.62 


33.42 


48.48 


33.63 


59 


60 


49.74 


33.55 


49.60 


33.77 


49.45 


33.98 


49.30 


34.20 


60 


61 


50.57 


34.11 


50.42 


34.33 


50.27 


34.55 


50.12 


34.77 


61 


62 


51.40 


34.67 


51.25 


34.89 


51.10 


35.12 


50.94 


35.34 


62 


63 


52.23 


35.23 


52.08 


35.46 


51.92 


35.68 


51.76 


35.91 


63 


64 


53.06 


35.79 


52.90 


36.02 


52.74 


36.25 


52.59 


36.48 


64 


65 


53.89 


36.35 


53.73 


36.58 


53.57 


36.82 


53.41 


37.05 


65 


66 


54.72 


36.91 


54.55 


37.15 


54.39 


37.38 


54.23 


37.62 


66 


67 


55.55 


37.46 


55.38 


37.71 


55.22 


37.95 


55.05 


38.19 


67 


68 


56.37 


38.03 


56.21 


38.27 


56.04 


38.52 


55.87 


38.76 


68 


69 


57.20 


38.58 


57.03 


38.83 


56.86 


39.08 


56.69 


39.33 


69 


70 


58.03 


39.14 


57.86 


39.40 


57.69 


39.65 


57.52 


39.90 


70 


71 


58.86 


39.70 


58.69 


39.96 


58.51 


40.21 


58.34 


40.47 


71 


72 


59.69 


40.26 


59.51 


40.52 


59.34 


40.78 


59.16 


41.04 


72 


73 


60.52 


40.82 


60.34 


41.08 


60.16 


41.35 


59.98 


41.61 


73 


74 


61.35 


41.38 


61.17 


41.65 


60.99 


41.91 


60.80 


42.18 


74 


75 


62.18 


41.94 


61.99 


42.21 


61.81 


42.48 


61.62 


42.75 


75 


76 


63.01 


42.50 


62.82 


42.77 


62.63 


43.05 


62.45 


43.32 


76 


77 


63.84 


43.06 


63.65 


43.34 


63.46 


43.61 


63.27 


43.89 


77 


78 


64.66 


43.62 


64.47 


43.90 


64.28 


44.18 


64.09 


44.46 


78 


79 


65.49 


44.18 


65.30 


44.46 


65.11 


44.75 


64.91 


45.03 


79 


80 


66.32 


44.74 


66.13 


45.02 


65.93 


45.31 


65.73 


45.60 


80 


81 


67.15 


45.29 


66.95 


45.59 


66.75 


45.88 


66.55 


46.17 


81 


82 


67.98 


45.85 


67.78 


46.15 


67.58 


46.45 


67.37 


46.74 


82 


83 


68.81 


46.41 


68.61 


46.71 


68.40 


47.01 


68.20 


47.31 


83 


84 


69.64 


46.97 


69.43 


47.28 


69.23 


47.58 


69.02 


47.88 


84 


85 


70.47 


47.53 


70.26 


47.84 


70.05 


48.14 


69.84 


48.45 


85 


86 


71.30 


48.09 


71.09 


48.40 


70.87 


48.71 


70.66 


49.02 


86 


87 


72.13 


48.65 


71.91 


48.96 


71.70 


49.28 


71.48 


49.59 


87 


88 


72.96 


49.21 


72.74 


49.53 


72.52 


49.84 


72.30 


50.16 


88 


89 


73.78 


49.77 


73.57 


50.09 


73.35 


50.41 


73.13 


50.73 


89 


90 


74.61 


50.33 


74.39 


50.65 


74.17 


50.98 


73.95 


51.30 


90 


91 


75.44 


50.89 


75.22 


51.22 


75.00 


51.54 


74.77 


51.87 


91 


92 


76.27 


51.45 


76.05 


51.78 


75.82 


52.11 


75.59 


52.44 


92 


93 


77.10 


52.00 


76.87 


52.34 


76.64 


52.68 


76.41 


53.01 


93 


94 


77.93 


52.56 


77.70 


52.90 


77.47 


53.24 


77.23 


53.58 


94 


95 


78.76 


53.12 


78.53 


53.47 


78.29 


53.81 


78.06 


54.15 


95 


96 


79.59 


53.68 


79.35 


54.03 


79.12 


54.37 


78.88 


54.72 


96 


97 


80.42 


54.24 


80.18 


54.59 


79.94 


54.94 


79.70 


55.29 


97 


98 


81.25 


54.80 


81.01 


55.15 


80.76 


55.51 


80.52 


55.86 


98 


99 


82.07 


55.36 


81.83 


55.72 


81.59 


56.07 


81.34 


56.43 


99 


100 


82.90 


55.92 


82.66 


56.28 


82.41 


56.64 


82.16 


57.00 


100 


6 
a 

a 

ei 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


£ 

o 

1 
s 


56 Deg. 


55} Deg. 


55* Deg. 


55* Deg. 



TRAVERSE TABLE. 



g 

1 

a 

(8 


35Deg 


35* Deg. 


35^ Deg. 


35} Deg. 


d 

a 


Lat. I Dep. 


Lat. 


Dep. 


Lat. 1 


Dep. 


Lat. 


Dep. 


1 


0.82 


0.57 


0.82 


0.58 


0.81 


0.58 


0.81 


0.58 


1 


2 


1.64 


1.15 


1.63 


1.15 


1.63 


1.16 


1.62 


1.17 


2 


3 


2.46 


1.72 


2.45 


1.73 


2.44 


1.74 


2.43 


1.75 


3 


4 


3.28 


2.29 


3.27 


2.31 


3.26 


2.32 


3.25 


2.34 


4 


5 


4.10 


2.87 


4.08 


2.89 


4.07 


2.90 


4.06 


2.92 


5 


6 


4.91 


3.44 


4.90 


3.46 


4.88 


3.48 


4.87 


3.51 


6 


7 


5.73 


4.01 


5.72 


4.04 


5.70 


4.06 


5.68 


4.09 


7 


8 


6.55 


4.59 


6.53 


4.62 


6.51 


4.65 


6.49 


4.67 


8 


9 


7.37 


5.16 


7.35 


5.19 


7.33 


5.23 


7.30 


5.26 


9 


10 | 8.19 


5.74 


8.17 


5.77 


8.14 


5.81 


8.12 


5.84 


10 


11 ' 9.01 


6.31 


8.98 


6.35 


8.96 


6.39 


8.93 


6.43 


11 


12 I 9.83 


6.88 


9.80 


6.93 


9.77 


6.97 


9.74 


7.01 


12 


13 ! 10.65 


7.46 


10.62 


7.50 


10.58 


7.55 


10.55 


7.60 


13 


14 


11.47 


8.03 


11.43 


8.08 


11.40 


8.13 


11.36 


8.18 


14 


15 


12.29 


8.60 


12.25 


8.66 


12.21 


8.71 


12.17 


8.76 


15 


16 


13.11 


9.18 


13.07 


9.23 


13.03 


9.29 


12.99 


9.35 


16 


17 


13.93 


9.75 


13.88 


9.81 


13.84 


9.87 


13.80 


9.93 


17 


18 


14.74 


10.32 


14-70 


10.39 


14.65 


10.45 


14.61 


10.52 


18 


19 


15.56 


10.90 


15.52 


10.97 


15.47 


11.03 


15.42 


11.10 


19 


20 


16.38 


11.47 


16.33 


11.54 


16.28 


11.61 


16.23 


11.68 


20 


21 


17.20 


12.05 


17.15 


12.12 


17.10 


12.19 


17.04 


12.27 


21 


22 


18.02 


12.62 


17.97 


12.70 


17.91 


12.78 


17.85 


12.85 


22 


23 


18.84 


13.19 


18.78 


13.27 


18.72 


13.36 


18.67 


13.44 


23 


24 


19.66 


13.77 


19.60 


13.85 


j 19.54 


13.94 


19.48 


14.02 


24 


25 


20.48 


14.34 


20.42 


14.43 


20.35 


14.52 


20.29 


14.61 


25 


26 


21.30 


14.91 


21.23 


15.01 


21.17 


15.10 


21.10 


15.19 


26 


27 


22.12 


15.49 


22.05 


15.58 


21.98 


15.68 


21.91 


15.77 


27 


28 


22.94 


16.06 


22.87 


16.16 


22.80 


16.26 


22.72 


16.36 


28 


29 


23.76 


16.63 


23.68 


16.74 


23.61 


16.84 


23.54 


16.94 


29 


30 


24.57 


17.21 


24.50 


17.31 


24.42 


17.42 


24.35 


17.53 


30 


31 


25.39 


17.78 


25.32 


17.89 


25.24 


18.00 


25.16 


18.11 


31 


32 


26.21 


18.35 


26.13 


18.47 


26.05 


18.58 


25.97 


18.70 


32 


33 


27.03 


18.93 


26.95 


19.05 


26.87 


19.16 


26.78 


19.28 


33 


34 


27.85 


19.50 


27.77 


19.62 


' 27.68 


19.74 


27.59 


19.86 


34 


35 


28.67 


20.08 


28.58 


20.20 


> 28.49 


20.32 


28.41 


20.45 


35 


36 


29.49 


20.65 


29.40 


20.78 


29.31 


20.91 


29.22 


21.03 


36 


37 


30.31 


21.22 


30.22 


21.35 


| 30.12 


21.49 


30.03 


21.62 


37 


38 


31.13 


21.80 


31.03 


21.93 


: 30.94 


22.07 


30.84 


22.20 


38 


39 


31.95 


22.37 


31.85 


22.51 


I 31.75 


22.65 


31.65 


22.79 


39 


40 


32.77 


22.94 


32.67 


23.09 


1 32.56 


23.23 


32.46 


23.37 


40 


41 


33.59 


23.52 


33.48 


23.66 


j 33.38 


23.81 


33.27 


23.95 


41 


42 


34.40 


24.09 


34.30 


24.24 


34.19 


24.39 


34.09 


24.54 


42 


43 


35.22 


24.66 


35.12 


24.82 


l| 35.01 


24.97 


34.90 


25.12 


43 


44 


36.04 


25.24 


35.93 


25.39 


il 35.82 


25.55 


35.71 


25.71 


44 


45 


36.86 


25.81 


36.75 


25.97 


!i 36.64 


26.13 


36.52 


26.29 


45 


46 


37.68 


26.38 


37.57 


26.55 


! 37.45 


26.71 


37.33 


26.88 


4G 


47 


38.50 


26.96 


38.38 


27.13 


38.26 


27.29 


38.14 


27.46 


47 


48 


39.32 


27.53 


39.20 


27.70 


|! 39.08 


27.87 


38.96 


28.04 


J!) 


49 


40.14 


28.11 


40.02 


28.28 


39.89 


28.45 


39.77 


28.63 


40 


50 


40.96 


28.68 


40.83 


28.86 


40.71 

li 


29.04 


40.58 


29.21 


50 


o 
c 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


1 Dep. 


Lat. 


Dep. 


Lat. 




55 Deg. 


54, 


Deg. 


54* 


Deg. 


54* 


Deg. 



TRAVERSE TABLE. 



73 



3 
O 


35 Deg. 


35* Deg. 


35* Deg. 


35| Deg. 


to 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


41.78 


29.25 


41.65 


29.43 


41.52 


29.62 


1 41.39 


29.80 


51 


52 


42.60 


29.83 


42.47 


30.01 


42.33 


30.20 


42.20 


30.38 


52 


53 


43.42 


30.40 


43.28 


30.59 


43.15 


30.78 


43.01 


30.97 


53 


54 


44.23 


30.97 


44.10 


31.17 


43.96 


31.36 


43.82 


31.55 


54 


1 55 


45.05 


31.55 


44.92 


31.74 


44.78 


31.94 


44.64 


32.13 


55 


1 56 


45.87 


32.12 


45.73 


32.32 


45.59 


32.52 


45.45 


32.72 


56 


1 57 


46.69 


32.69 


46.55 


32.90 


46.40 


33.10 


46.26 


33.30 


57 


t 58 


47.51 


33.27 


47.37 


33.47 


47.22 


33.68 


47.07 


33.89 


58 


1 59 


48.33 


33.84 


48.18 


34.05 


48.03 


34.26 


47.88 


34.47 


59 


60 


49.15 


34.41 


49.00 


34.63 


48.85 


34.84 


48.69 


35.05 


60 


61 


49.97 


34.99 


49.82 


35.21 


49.66 


35.42 


49.51 


35.64 


61 


62 


50.79 


35.56 


50.63 


35.78 


50.48 


36.00 


50.32 


36.22 


62 


63 


51.61 


36.14 


51.45 


36.36 


51.29 


36.58 


51.13 


36.81 


63 


64 


52.43 


36.71 


52.27 


36.94 


52.10 


37.16 


51.94 


37.39 


64 


65 


53.24 


37.28 


53.08 


37.51 


52.92 


37.75 


52.75 


37.98 


65 


65 


54.06 


37.86 


53.90 


38.09 


53.73 


38.33 


53.56 


38.56 


66 


67 


54.88 


38.43 


54.71 


38.67 


54.55 


38.91 


54.38 


39.14 


67 


68 


55.70 


39.00 


55.53 


39.25 


55.36 


39.49 


55.19 


39.73 


68 


69 


56,52 


39.58 


56.35 


39.82 


56.17 


40.07 


56.00 


40.31 


69 


70 


57.34 


40.15 


57.16 


40-40 


56.99 


40.65 


56.81 


40.90 


70 


71 


58.16 ! 40.72 


57.98 


40.98 


57.80 


41.23 


57.62 


41.48 


71 


72 


58.98 


41.30 


58.80 


41.55 


58.62 


41.81 


58.43 


42.07 


72 


73 


59.80 


41.87 


59.61 


42.13 


59.43 


42.39 


59.24 


42.65 


73 


74 


60.62 


42.44 


60.43 


42.71 


60.24 


42.97 


60.06 


43.23 


74 


75 


61.44 


43.02 


61.25 


43.29 


61.06 


43.55 


60.87 


43.82 


75 


76 


62.26 


43.59 


62.06 


43.86 


61.87 


44.13 


61.68 


44.40 


76 


77 


63.07 


44.17 


62.88 


44.44 


62.69 


44.71 


62.49 


44.99 


77 


78 


63.89 


44.74 


63.70 


45.02 


63.50 


45.29 


63.30 


45.57 


78 


79 


64.71 


45.31 


64.51 


45.59 


64.32 


45.88 


64.11 


46.16 


79 


80 


65.53 


45.89 


65.33 


46.17 


65.13 


46.46 


64.93 


46.74 


80 


81 


66.35 


46.46 


66.15 


46.75 


65.94 


47.04 


65.74 


47.32 


81 


82 


67.17 


47.03 


66.96 


47.33 


66.76 


47.62 


66.55 


47.91 


82 


83 


67.99 


47.61 


67.78 


47.90 


67.57 


48.20 


67.36 


48.49 


83 


84 


68.81 


48.18 


68.60 


48.48 


68.39 


48.78 


68.17 


49.08 


84 


85 


69.63 


48.75 


69.41 


49.06 


69.20 


49.36 


P8.98 


49.66 


85 


86 


70.45 


49.33 


70.23 


49.63 


70.01 


49.94 


69.80 


50.25 


86 


87 


71.27 


49.90 


71.05 


50.21 


70.83 


50.52 


70.61 


50.83 


87 


88 


72.09 


50.47 


71.86 


50.79 


71.64 


51. 1» 


71.42 


51.41 


88 


89 


72.90 


51.05 


72.68 


51.37 


72.46 


51.68 


72.23 


52.00 


89 


90 


73.72 


51.62 


73.50 


51.94 


73.27 


52.26 


73.04 


52.58 


90 


91 


74.54 


52.20 


74.31 


52.52 


74.08 


52.84 


73.85 


53.17 


91 


92 


75.36 


52.77 


75.13 


53.10 


74.90 


53.42 


74.66 


53.75 


92 


93 


76.18 


53.34 


75.95 


53.67 


75.71 


54.01 


75.48 


54.34 


93 


94 


77.00 


53.92 


76.76 


54.25 


76.53 


54.59 


76.29 


54.92 


94 


95 


77.82 


54.49 


77.58 


54.83 


77.34 


55.17 


77.10 


55.50 


95 


96 


78.64 


55.06 


78.40 


55.41 


78.16 


55.75 


77.91 


56.09 


96 


97 


79.46 


55.64 


79.21 


55.98 


78.97 


56.33 


78.72 


56.67 


97 


98 


80.28 


56.21 


80.03 


56.56 


79.78 


56.91 


79.53 


57.26 


98 


99 


81.10 


56.78 


80.85 


57.14 


80.60 


57.49 


80.35 


57.84 


99 


100 


81.92 


57.36 


81.66 


57.71 


81.41 


58.07 


81.16 


58.42 


100 


o 

a 

3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. 


Dep. 


Lat. 


o 
o 

a 


55 Deg. 


54} Deg. 


54£ Deg. 


S4i Deg. 



30* 



2Y 



74 



TRAVERSE TABLE. 



— 
o 

B" 

£ 

o 


36 Deg. 


364, Deg. 


36i Deg. 


36| Deg. 


g 

a 
o 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.81 


0.59 


0.81 


0.59 


0.80 


0.59 


0.80 


0.60 


1 


2 


1.62 


1.18 


1.61 


1.18 


1.61 


1.19 


1.60 


1.20 


2 


3 


2.43 


1.76 


2.42 


1.77 


2.41 


1.78 


2.40 


1.79 


3 


4 


3.24 


2.35 


3.23 


2.37 


3.22 


2.38 


3.20 


2.39 


4 


5 


4.05 


2.94 


4.03 


2.96 


4.02 


2.97 


4.01 


2.99 


5 


6 


4.85 


3.53 


4.84 


3.55 


4.82 


3.57 


4.81 


3.59 


6 


7 


5.66 


4.11 


5.65 


4.14 


5.63 


4.16 


5.61 


4.19 


7 


8 


6.47 


4.70 


6 45 


4.73 


6.43 


4.76 


6.41 


4.79 


8 


9 


7.28 


5.29 


7.26 


5.32 


7.23 


5.35 


7.21 


5.38 


9 | 


10 


8.09 


5.88 


8.06 


5.91 


8.04 


5.95 


8.01 


5.98 


10 


11 


8.90 


6.47 


8.87 


6.50 


8.84 


6.54 


8.81 


6.58 


11 


12 


9.71 


7.05 


9.68 


7.10 


9.65 


7.14 


9.61 


7.18 


12 


13 


10.52 


7.64 


10-48 


7.69 


10.45 


7.73 


10.42 


7.78 


13 


14 


11.33 


8.23 


11.29 


8.28 


11.25 


8.33 


11.22 


8.38 


14 


15 


12.14 


8.82 


12.10 


8.87 


12.06 


8.92 


12.02 


8.97 


15 


16 


12.94 


9.40 


12.90 


9.46 


12.86 


9.52 


12.82 


9.57 


16 


17 


13.75 


9.99 


13.71 


10.05 


13.67 


10.11 


13.62 


10.17 


17 


18 


14.56 


10.58 


14.52 


10.64 


14.47 


10.71 


14.42 


10.77 


18 


1 19 


15.37 


11.17 


15.32 


11.23 


15.27 


11.30 


15.22 


11.37 


19 


20 


16.18 


11.76 


16.13 


11.83 


16.08 


11.90 


16.03 


11.97 


20 


21 


16.99 


12.34 


16.94 


12.42 


16.88 


12.49 


16.83 


12.56 


21 


22 


17.80 


12.93 


17.74 


13.01 


17.68 


13.09 


17.63 


13.16 


22 


23 


18.61 


13.52 


18.55 


13.60 


18.49 


13.68 


18.43 


13.76 


23 


24 


19.42 


14.11 


19.35 


14.19 


19.29 


14.28 


19.23 


14.36 


24 


25 


20.23 


14.69 


20.16 


14.78 


20.10 


14.87 


20.03 


14.96 


25 


26 


21.03 


15.28 


20.97 


15.37 


20.90 


15.47 


20.83 


15.56 


26 


27 


21.84 


15.87 


21.77 


15.97 


21.70 


16.06 


21.63 


16.15 


27 


28 


22.65 


16.46 


22.58 


16.56 


22.51 


16.65 


22.44 


16.75 


28 


29 


23.46 


17.05 


23.39 


17.15 


23.31 


17.25 


23.24 


17.35 


29 


30 


24.27 


17.63 


24.19 


17.74 


24.12 


17.84 


24.04 


17.95 


30 


31 


25.08 


18.22 


25.00 


18.33 


24.92 


18.44 


24.84' 


18.55 


31 | 


32 


25.89 


18.81 ' 


25.81 


13.92 


25.72 


19.03 


25.64 


19.15 


32 1 


33 


26.70 


19.40 


26.61 


19.51 


26.53 


19.63 


26.44 


19.74 


33 


34 


27.51 


19.98 : 


27.42 


20.10 


27.33 


20.22 


27.24 


20.34 


34 


35 


23.32 


20.57 


28.23 


20.70 


28.13 


20.82 


28.04 


20.94 


35 


36 


29.12 


21.16 


29.03 


21 .29 


23.94 


21.41 


28.85 


21-54 


36 ! 


37 


29.93 


21.75 


29.34 


21.88 


29.74 


22.01 


29.65 


82.14 


37 : 


38 


30.74 


22.34 


30.64 


22.47 


30.55 


22.60 


30.45 


22.74 


30 


39 


31.55 


22.92 


31.45 


23.06 


31.35 


23.20 


31.25 


23.33 


39 i 


40 


32.36 


23.51 


32.26 


23.65 


32.15 


23.79 


32.05 


83.93 


40 j 


41 


33.17 


24.10 


33.06 


24.24 


32.96 


24.39 


32.85 


24.53 


41 


42 


33.93 


24.69 


33.87 


24.83 


33.76 


24.98 


33.65 


25.13 


42! 


43 


34.79 


25.27 


34.68 


25.43 


34.57 


25.58 


34.45 


25.73 


43 


44 


35.60 


25.86 


35.48 


26.02 


35.37 


26.17 


35.26 


26.33 


44 


45 


36.41 


26.45 


36.29 


26.61 


36.17 


26.77 


36.06 


26.92 


45 


46 


37.21 


27.04 


37.10 


27.20 


36.93 


27.36 


36.86 


27.52 


46 


47 


33.02 


27.63 


37.90 


27.79 


37.78 


27.96 


37.66 


28.12 


47 


48 


38.83 


28.21 


38.71 


28.38 


38.59 


28.55 


38.46 


28.72 


48 


49 


39.64 


28.80 


39.52 


28.97 


39.39 


29.15 


39.26 


29.32 


49 


50 


40.45 


29.39 


40.32 


29.57 


40.19 


29.74 


40.06 


29.92 


50 

« 

a 
1 
5 


i 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


54 Deg. 


53| 


Deg. 


53i Deg. 


53i Deg. 



TRAVERSE TABLE. 



75 



g 

B 

a 
? 


36 Deg. 


36i Deg. 


36£ Deg. 


36| Deg. 


g 

if 

o 

? 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




51 


41.26 


29.98 


41.13 


30.16 


41.00 


30.34 


40.86 


30.51 


51 




52 


42.07 


30.56 


41.94 


30.75 


41.80 


30.93 


41.67 


31.11 


52 




53 


42.88 


31.15 


42.74 


31.34 


42.60 


31.53 


42.47 


31.71 


53 




54 


43.69 


31.74 


43.55 


31.93 


43.41 


32.12 


43.27 


32.31 


54 




55 


44.50 


32.33 


44.35 


32.52 


44.21 


32.72 


44.07 


32.91 


55 




56 


45.30 


32.92 


45.16 


33.11 


45.02 


33.31 


44.87 


33.51 


56 




57 


46.11 


33.50 


45.97 


33.70 


45.82 


33.90 


45.67 


34.10 


57 




58 


46.92 


34.09 


46.77 


34.30 


46.62 


34.50 


46.47 


34.70 


58 




59 


47.73 


34.68 


47.58 


34.89 


47.43 


35.09 


47.27 


35.30 


59 




60 


48.54 


35.27 


48.39 


35.48 


48.23 


35.69 


48.08 


35.90 


60 




61 


49.35 


35.85 


49.19 


36.07 


49.04 


36.28 


48.88 


36.50 


61 




62 


50.16 


36.44 


50.00 


36.66 


49.84 


36.88 


49.68 


37.10 


62 




63 


50.97 


37.03 


50.81 


37.25 


50.64 


37.47 


50.48 


37.69 


63 




64 


51.78 


37.62 


51.61 


37.84 


51.45 


38.07 


51.28 


38.29 


64 




65 


52.59 


38.21 


52.42 


38.44 


52.25 


38.66 


52.08 


38.89 


65 




66 


53.40 


38.79 


53.23 


39.03 


53.05 


39.26 


52.88 


39.49 


66 




67 


54.20 


39.38 


54.03 


39.62 


53.86 


39.85 


53.68 


40.09 


67 




68 


55.01 


39.97 


54.84 


40.21 


54.66 


40.45 


54.49 


40.69 


68 




69 


55.82 


40.56 


55.64 


40.80 


55.47 


41.04 


55.29 


41.28 


69 




70 


56.63 


41.14 


56.45 


41.39 


56.27 


41.64 


56.09 


41.88 


70 




71 


57.44 


41.73 


57.26 


41.98 


57.07 


42.23 


56.89 


42.48 


71 




72 


58.25 


42.32 


58.06 


42.57 


57.88 


42.83 


57.69 


43.08 


72 




13 


59.06 


42.91 


58.87 


43.17 


58.68 


43.42 


58.49 


43.68 


73 




Y4 


59.87 


43.50 


59.68 


43.76 


59.49 


44.02 


59.29 


44.28 


74 




75 


60.68 


44.08 


60.48 


44.35 


60.29 


44.61 


60.09 


44.87 


75 




76 


61.49 


44.67 


61.29 


44.94 


61.09 


45.21 


60.90 


45.47 


76 




77 


62.29 


45.26 


62.10 


45.53 


61.90 


45.80 


61.70 


46.07 


77 




78 


63.10 


45.85 


62.90 


46.12 


62.70 


46.40 


62.50 


46.67 


78 




79 


63.91 


46.43 


63.71 


46.71 


63.50 


46.99 


63.30 


47.27 


79 




80 


64.72 


47.02 


64.52 


47.30 


64.31 


47.59 


64.10 


47.87 


80 




81 


65.53 


47.61 


65.32 


47.90 


65.11 


48.18 


64.90 


48.46 


81 




82 


66.34 


48.20 


66.13 


48.49 


65.92 


48.78 


65.70 


49.06 


82 




83 


67.15 


48.79 


66.93 


49.08 


66.72 


49.37 


66.50 


49.66 


83 




84 


67.96 


49.37 


67.74 


49.67 


67.52 


49.97 


67.31 


50.26 


84 




85 


68.77 


49.96 


68.55 


50.26 


68.33 


50.56 


68.11 


50.86 


85 




86 


69.58 


50.55 


69.35 


50.85 


69.13 


51.15 


68.91 


51.46 


86 




87 


70.38 


51.14 


70.16 


51.44 


69.94 


51.75 


69.71 


52.05 


87 




88 


71.19 


51.73 


70.97 


52.04 


70.74 


52.34 


70.51 


52.65 


88 




89 


72.00 


52.31 


71.77 


52.63 


71.54 


52.94 


71.31 


53.25 


89 




90 


72.81 


52.90 


72.58 


53.22 


72.35 


53.53 


72.11 


53.85 


90 




91 


73.62 


53.49 


73.39 


53.81 


73.15 


54.13 


72.91 


54.45 


91 




92 


74.43 


54.08 


74.19 


54.40 


73.95 


54.72 


73.72 


55.05 


92 




93 


75.24 


54.66 


75.00 


54.99 


74.76 


55.32 


74.52 


55.64 


93 




94 


76.05 


55.25 


75.81 


55.58 


75.56 


55.91 


75.32 


56.24 


94 




95 


76.86 


55.84 


76.61 


56.17 


76.37 


56.51 


76.12 


56.84 


95 




96 


77.67 


56.43 


77.42 


56.77 


77.17 


57.10 


76.92 


57.44 


96 




97 


78.47 


57.02 


78.23 


57.36 


77.97 


57.70 


77.72 


58.04 


97 




98 


79.28 


57.60 


79.03 


57.95 


78.78 


58.29 


78.52 


58.64 


98 




99 


80.09 


58.19 


79.84 


58.54 


79.58 


58.89 


79.32 


59.23 


99 




100 


80.90 


58.78 


80.64 


59.13 


80.39 


59.48 


80.13 


59.83 


100 




o 

a 

5 

■ 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

a 
* 

5 




54 1 


)eg. 


53| 


Deg. 


53J Deg. 


53* Deg. 





76 



TRAVERSE TABLE. 



g 

s 

a 
o 

a 


37 Deg. 


37* Deg. 


37* Deg. 


37J Deg 


q 

1 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


a 




1 


0.80 


0.60 


0.80 


0.61 


0.79 


0.61 


0.79 


0.61 


1 




2 


1.60 


1.20 


1.59 


1.21 


1.59 


1.22 


1.58 


1.22 


2 




3 


2.40 


1.81 


2.39 


1.82 


2.38 


1.83 


2.37 


1.84 


3 




4 


3.19 


2.41 


3.18 


2.42 


3.17 


2.43 


3.16 


2.45 


4 




5 


3.99 


3.01 


3.98 


3.03 


3.97 


3.04 


3.95 


3.06 


5 




6 


4.79 


3.61 


4.78 


3.63 


4.76 


3.65 


4.74 


3.67 


6 




7 


5.59 


4.21 


5.57 


4.24 


5.55 


4.26 


5.53 


4.29 


7 




8 


6.39 


4.81 


6.37 


4.84 


6.35 


4.87 


6.33 


4.90 


8 




9 


7.19 


5.42 


7.16 


5.45 


7.14 


5.48 


7.12 


5.51 


9 




10 


7.99 


6.02 


7.96 


6.05 


7.93 


6.09 


7.91 


6.12 


10 




11 


8.78 


6.62 


8.76 


6.66 


8.73 


6.70 


8.70 


6.73 


11 




12 


9.58 


7.22 


9.55 


7.26 


9.52 


7.31 


9.49 


7.35 


12 




13 


10.38 


7.82 


10.35 


7.87 


10.31 


7.91 


10.28 


7.96 


13 




14 


11.18 


8-43 


11.14 


8.47 


11.11 


8.52 


11.07 


8.57 


14 




15 


11.98 


9.03 


11.94 


9.08 


11.90 


9.13 


11.86 


9.18 


15 




16 


12.78 


9.63 


12.74 


9.68 


12.69 


9.74 


12.65 


9.80 


16 




17 


13.58 


10.23 


13.53 


10.29 


13.49 


10.35 


13.44 


10.41 


17 




18 


14.38 


10.83 


14.33 


10.90 


14.28 


10.96 


14.23 


11.02 


18 




19 


15.17 


11.43 


15.12 


11.50 


15.07 


11.57 


15.02 


11.63 


19 




20 15.97 


12.04 


15.92 


12.11 


15.87 


12.18 


15.81 


12.24 


20 




21 16.77 


12.64 


16.72 


12.71 


16.66 


12.78 


16.60 


12.86 


21 




22 


17.57 


13.24 


17.51 


13.32 


17.45 


13.39 


17.40 


13.47 


22 




23 


18.37 


13.84 


18.31 


13.92 


18.25 


14.00 


18.19 


14.08 


23 




24 


19.17 


14.44 


19.10 


14.53 


19.04 


14.61 


18.98 


14.69 


24 




25 


19 97 


15.05 


19.90 


15.13 


19.83 


15.22 


19.77 


15.31 


25 




26 


20.76 


15.65 


20.70 


15.74 


20.63 


15.83 


20.56 


15-92 


26 




27 


21.56 


16.25 


21.49 


16.34 


21.42 


16.44 


21.35 


16.53 


27 




28 


22.36 


16.85 


22.29 


16.95 


22.21 


17.05 


22.14 


17.14 


28 




29 


23.16 


17.45 


23.08 


17.55 


23.01 


17.65 


22.93 


17.75 


29 




30 


23.96 


18.05 


23.88 


18.16 


23.80 


18.26 


23.72 


18.37 


30 




31 


24.76 


18.66 


24.68 


18.76 


24.59 


18.87 


24.51 


18.98 


31 




32 


25.56 


19.26 


25.47 


19.37 


25.39 


19.48 


25.30 


19.59 


32 




33 


26.35 


19.86 


26.27 


19.97 


26.18 


20.09 


26.09 


20.20 


33 




34 


27.15 


20.46 


27.06 


20.58 


26.97 


20.70 


26.88 


20.82 


34 




35 


27.95 


21.06 


27.86 


21.19 


27.77 


21.31 


27.67 


21.43 


35 




36 


28.75 


21.67 


28.66 


21.79 


:; 28.56 


21.92 


28.46 


22.04 


36 




37 


29.55 


22.27 


29.45 


22.40 


i : 29.35 


22.52 


29.26 


22.65 


37 




38 


30.35 


22.87 


1 30.25 


23.00 


! 30.15 


23.13 


30.05 


23.26 


38 




39 


31.15 


23.47 


I 31.04 


23.61 


1 30.94 


23.74 


30.84 


23.88 


39 




40 


31.95 


24.07 


| 31.84 


24.21 


1 31.73 

) 


24.35 


31.63 


24.49 


40 




41 


32.74 


24.67 


32.64 


24.82 


' 32.53 


24.96 


32.42 


25.10 


41 




42 


33.54 


25.28 


33.43 


25.42 


! 33.32 


25.57 


33.21 


25.71 


42 




43 


34.34 


25.88 


1 34.23 


26.03 


34.11 


26.18 


34.00 


26.33 


43 




44 


35.14 


26.43 


1 35.02 


26.63 


34.91 


26.79 


34.79 


26.94 


44 




45 


35.94 


27.03 


| 35.82 


27.24 


35.70 


27.39 


35.58 


27.55 


45 




46 


36.74 


27.68 


36.62 


27.84 


36.49 


28.00 


36.37 


28.16 


46 




47 


37.54 


28.29 


i 37.41 


28.45 


37.29 


28.61 


37.16 


28.77 


47 




48 


38.33 


28.89 


38.21 


29.05 


38.08 


29.22 


37.95 


29.39 


in 




49 


39.13 


29.49 


, 33.00 


29.66 


38.87 


29.83 


38.74 


30.00 


49 




50 


39.93 


30.09 


33.80 


30.26 


39.67 


30.44 


39.53 


30.61 


50 




o 

a 
a 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 

(5 




53 Deg. 


52J Deg. 


1 

52i Deg. 


52$ Deg. 





TRAVERSE TABLE. 



77 





o 

a 
a 
ID 


37 Deg. 


37} Deg. 


374 


Deg. 


37| Deg. 


p 

3 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




51 


40.73 


30.69 


40.60 


30.87 


40.46 


31.05 


40.33 


31.22 


51 




52 


41.53 


31.29 


41.39 


31.48 


41.25 


31.66 


41.12 


31.84 


52 \ 




53 


42.33 


31.90 


42.19 


32.08 


42.05 


32.26 


41.91 


32.45 


53 




54 


43.13 


32.50 


42.98 


32.69 


42.84 


32.87 


42.70 


33.06 


8 

55 




55 


43.92 


33.10 


43.78 


33.29 


43.63 


33.48 


43.49 


33.67 




56 


44.72 


33.70 


44.58 


33.90 


44.43 


34.09 


44.28 


34.28 


56 




57 


45.52 


34.30 


45.37 


34.50 


45.22 


34.70 


45.07 


34.90 


57 




58 


46.32 


34.91 


46.17 


35.11 


46.01 


35.31 


45.86 


35.51 


58 




59 


47.12 


35.51 


46.96 


35.71 


46.81 


35.92 


46.65 


36.12 


59 




60 


47.92 


36.11 


47.76 


36.32 


47.60 


36.53 


47.44 


36.73 


60 




61 


48.72 


36.71 


48.56 


36.92 


48.39 


37.13 


48.23 


37.35 


61 




62 


49.52 


37.31 


49.35 


37.53 


49.19 


37.74 


49.02 


37.96 


62 




63 


50.31 


37.91 


50.15 


38.13 


49.98 


38.35 


49.81 


38.57 


63 




64 


51.11 


38.52 


50.94 


38.74 


50.77 


38.96 


50.60 


39.18 


64 




65 


51.91 


39.12 


51.74 


39.34 


51.57 


39.57 


51.39 


39.79 


65 




66 


52.71 


39.72 


52.54 


39.95 


52.36 


40.18 


52.19 


40.41 


66 




67 


53.51 


40.32 


53.33 


40.55 


53.15 


40.79 


52.98 


41.02 


67 




68 


54.31 


40.92 


54.13 


41.16 


53.95 


41.40 


53.77 


41.63 


68 




69 


55.11 


41.53 


54.92 


41.77 


54.74 


42.00 


54.56 


42.24 


69 ■ 




70 


55.90 


42.13 


55.72 


42.37 


55.53 


42.61 


55.35 


42.86 


70 . 




71 


56.70 


42.73 


56.52 


42.98 


56.33 


43.22 


56.14 


43.47 


71 




72 


57.50 


43.33 


57.31 


43.58 


57.12 


43.83 


56.93 


44.08 


72 1 




73 


58.30 


43.93 


58.11 


44.19 


57.91 


44.44 


57.72 


44.69 


73 




74 


59.10 


44.53 


58.90 


44.79 


58.71 


45.05 


58.51 


45.30 


74 




75 


59.90 


45.14 


59.70 


45.40 


59.50 


45.66 


59.30 


45.92 


75 ■ 




76 


60.70 


45.74 


60.50 


46.00 


60.29 


46.27 


60.09 


46.53 


76 




77 


61.49 


46.34 


61.29 


46.61 


61.09 


46.87 


60.88 


47.14 


77 




78 


62.29 


46.94 


62.09 


47.21 


61.88 


47.48 


61.67 


47.75 


78 




79 


63.09 


47.54 


62.88 


47.82 


62.67 


48.09 


62.46 


48.37 


79 




80 


63.89 


48.15 


63.68 


48.42 


63.47 


48.70 


63.26 


48.98 


80 
81 




81 


64.69 


48.75 


64.48 


49.03 


64.26 


49-31 


64.05 


49.59 




82 


65.49 


49.35 


65.27 


49.63 


65.05 


49.92 


64.84 


50.20 


82 




83 


66.29 


49.95 


66.07 


50.24 


65.85 


50.53 


65.63 


50.81 


83 




84 


67.09 


50.55 


66.86 


50.84 


66.64 


51.14 


66.42 


51.43 


84 




85 


67.88 


51.15 


67.66 


51.45 


67.43 


51.74 


67.21 


52.04 


85 . 




86 


68.68 


51.76 


68.46 


52.06 


68.23 


52.35 


68.00 


52.65 


86 




87 


69.48 


52.36 


69.25 


52.66 


69.02 


52.96 


68.79 


53.26 


87 




88 


70.28 


52.96 


70.05 


53.27 


69.82 


53.57 


69.58 


53.88 


88 




89 


71.08 


53.56 


70.84 


53.87 


70.61 


54.18 


70.37 


54.49 


89 




90 


71.88 


54.16 


71.64 


54.48 


71.40 


54.79 


71.16 


55.10 


90 




91 


72.68 


54.77 


72.44 


55.08 


72.20 


55.40 


71.95 


55.71 


91 




92 


73.47 


55.37 


73.23 


55.69 


72.99 


56.01 


72.74 


56.32 


92 




93 


74.27 


55.97 


74.03 


56.29 


73.78 


56.61 


73.53 


56.94 


93 




94 


75.07 


56.57 


74.82 


56.90 


74.58 


57.22 


74.32 


57.55 


94 




95 


75.87 


57.17 


75.62 


57.50 


75.37 


57.83 


75.12 


58.16 


95 




96 


76 67 


57.77 


76.42 


58.11 


76.16 


58.44 


75.91 


58.77 


96 




97 


77.47 


58.38 


77.21 


58.71 


76.96 


59.05 


76.70 


59.39 


97 




98 


78.27 


58.98 


78.01 


59.32 


77.75 


59.66 


77.49 


60.00 


98 




99 


79.06 


59.58 


78.80 


59.92 


78.54 


60.27 


78.28 


60.61 


99 




100 


79.86 


60.18 


79.60 


60.53 


79.34 


60.88 


79.07 


61.22 


100 




£ 

J 
5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


a 




53 Deg. 


52* Deg. 


52i Deg. 


52} 


Deg. 



TRAVERSE TABLE. 




TRAVERSE TABLE. 



79 



o 

3 


38 Deg. 


38* Deg. 


38* Deg. 


38| Deg. 


n 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


40.19 


31.40 


40.05 


31.57 


39.91 


31.75 


39.77 


31.92 


51 


52 


40.98 


32.01 


40.84 


32.19 


40.70 


32.37 


40.55 


32.55 


52 


53 


41.76 


32.63 


41.62 


32.81 


41.48 


32.99 


41.33 


33.17 


53 


54 


42.55 


33.25 


42.41 


33.43 


42.26 


33.62 


42.11 


33.80 


54 


55 


43.34 


33.86 


43.19 


34.05 


43.04 


34.24 


42.89 


34.43 


55 


56 


44.13 


34.48 


43.98 


34.67 


43.83 


34.86 


43.67 


35.05 


56 


57 


44.92 


35.09 


44.76 


35.29 


44.61 


35.48 


44.45 


35.68 


57 


58 


45.70 


35.71 


45.55 


35.91 


45.39 


36.11 


45.23 


36.30 


58 


59 


46.49 


36.32 


46.33 


36.53 


46.17 


36.73 


46.01 


36.93 


59 


60 


47.28 


36.94 


47.12 


37.15 


46.96 


37.35 


46.79 


37.56 


60 


61 


48.07 


37.56 


47.90 


37.76 


47.74 


37.97 


47.57 


38.18 


61 


62 


48.86 


38.17 


48.69 


38.38 


48.52 


38.60 


48.35 


38.81 


62 


63 


49.64 


38.79 


49.47 


39.00 


49.30 


39.22 


49.13 


39.43 


63 


64 


50.43 


39.40 


50.26 


39.62 


50.09 


39.84 


49.91 


40.06 


64 


65 


51.22 


40.02 


51.05 


40.24 


50.87 


40.46 


50.69 


40.68 


65 


66 


52.01 


40.63 


51.83 


40.86 


51.65 


41.09 


51.47 


41.31 


66 


67 


52.80 


41.25 


52.62 


41.48 


52.43 


41.71 


52.25 


41.94 


67 


68 


53.58 


41.86 


53.40 


42.10 


53.22 


42.33 


53.03 


42.56 


68 


69 


54.37 


42.48 


54.19 


42.72 


54.00 


42.95 


53.81 


43.19 


69 


70 


55.16 


43.10 


54.97 


43.34 


54.78 


43.58 


54.59 


43.81 


70 


71 


55.95 


43.71 


55.76 


43.96 


55.57 


44.20 


55.37 


44.44 


71 


72 


56.74 


44.33 


56.54 


44 57 


56.35 


44.82 


56.15 


45.07 


72 


73 


57.52 


44.94 


57.33 


45.19 


57.13 


45.44 


56.93 


45.69 


73 


74 


58.31 


45.56 


58.11 


45.81 


57.91 


46.07 


57.71 


46.32 


74 


75 


59.10 


46.17 


58.90 


46.43 


58.70 


46.69 


58.49 


46.94 


75 


76 


59.89 


46.79 


59.68 


47.05 


59.48 


47.31 


59.27 


47.57 


76 


77 


60.68 


47.41 


60.47 


47.67 


60.26 


47.93 


60.05 


48.20 


77 


78 


61.46 


48.02 


61.25 


48.29 


61.04 


48.56 


60.83 


48.82 


78 


79 


62.25 


48.64 


62.04 


48.91 


61.83 


49.18 


61.61 


49.45 


79 


80 


63.04 


49.25 


62.83 


49.53 


62.61 


49.80 


62.39 


50.07 


80 


81 


63.83 


49.87 


63.61 


50.15 


63.39 


50.42 


63.17 


50.70 


81 


82 


64.62 


50.48 


64.40 


50.77 


64.17 


51.05 


63.95 


51.33 


82 


83 


65.40 


51.10 


65.18 


51.38 


64.96 


51.67 


64.73 


51.95 


83 


84 


66.19 


51.72 


65.97 


52.00 


65.74 


52.29 


65.51 


52.58 


84 


85 


66.98 


52.33 


66.75 


52.62 


66.52 


52.91 


66.29 


53.20 


85 


86 


67.77 


52.95 


67.54 


53.24 


67.30 


53.54 


67.07 


53.83 


86 


87 


68.56 


53.56 


68.32 


53.86 


68.09 


54.16 


67.85 


54.46 


87 


88 


69.34 


54.18 


69.11 


54.48 


68.87 


54.78 


68.63 


55.08 


88 


89 


70.13 


54.79 


69.89 


55.10 


69.65 


55.40 


69.41 


55.71 


89 


90 


70.92 


55.41 


70.68 


55.72 


70.43 


56.03 


70.19 


56:33 


90 


' 91 


71.71 


56.03 


71.46 


56.34 


71.22 


56.65 


70.97 


56.96 


91 


92 


72.50 


56.64 


72.25 


56.96 


72.00 


57.27 


71.75 


57.58 


92 


93 


73.28 


57.26 


73.03 


57.58 


72.78 


57.89 


72.53 


58.21 


93 


94 


74.07 


57.87 


73.82 


58.19 


73.57 


58.52 


73.31 


58.84 


94 


95 


74.86 


58.49 


74.61 


58.81 


74.35 


59.14 


74.09 


59.46 


95 


96 


75.65 


59.10 


75.39 


59.43 


75.13 


59.76 


74.87 


60.09 


96 


97 


76.44 


59.72 


76.18 


60.05 


75.91 


60.33 


75.65 


60.71 


97 


98 


77.22 


60.33 


76.96 


60.67 


76.70 


61.01 


76.43 


61.34 


98 


99 


78.01 


60.95 


77.75 


61.29 


77.48 


61.63 


77.21 


61.97 


99 


100 


78.80 


61.57 


78.53 


61.91 


78.26 


62.25 


77.99 


62.59 


100 


o 

1 

5 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


» 

o 

a 

5 


52 1 


>eg. 


51} Deg. 


51i Deg. 


51| Deg. 



80 



TRAVERSE TABLE. 



3 

a 


39 


Deg. 


39* Deg. 


39i Deg. 


39 i leg. 


O 

V 

3 

? 
1 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

0.64 




j 


0.78 


0.63 


0.77 


0.63 


0.77 


0.64 


0.77 




2 


1.55 


1.26 


1.55 


1.27 


1.54 


1.27 


1.54 


1.28 


2 




3 


2.33 


1.89 


2.32 


1.90 


2.31 


1.91 


2.31 


1.92 


3 




4 


3.11 


2.52 


3.10 


2.53 


3.09 


2.54 


3.08 


2.56 


4 




5 


3.89 


3.15 


3.87 


3.16 


3.86 


3.18 


3.84 


3.20 


5 




6 


4.66 


3.78 


4.65 


3.80 


4.63 


3.82 


4.61 


3.84 


6 




7 


5.44 


4.41 


5.42 


4.43 


5.40 


4.45 


5.38 


4.48 


7 




8 


6.22 


5.03 


6.20 


5.06 


6.17 


5.09 


6.15 


5.12 


8 




9 


6.99 


5.66 


6.97 


5.69 


6.94 


5.72 


6.92 


5.75 


9 




10 


7.77 


6.29 


7.74 


6.33 


7.72 


6.36 


7.69 


6.39 


10 




11 


8.55 


6.92 


8.52 


6.96 


8.49 


7.00 


8.46 


7.03 


11 




12 


9.33 


7.55 


9.29 


7.59 


9.26 


7.63 


9.23 


7.67 


12 




13 


10.10 


8.18 


10.07 


8.23 


10.03 


8.27 


9.99 


8.31 


13 




14 


10.88 


8.81 


10.84 


8.86 


10.80 


8.91 


10.76 


8.95 


14 




15 


11.66 


9.44 


11.62 


9.49 


11.57 


9.54 


11.53 


9.59 


15 




16 


12.43 


10.07 


12.39 


10.12 


12.35 


10.18 


12.30 


10.23 


16 




17 


13.21 


10.70 


13.16 


10.76 


13.12 


10.81 


13.07 


10.87 


17 




18 


13.99 


11.33 


13.94 


11.39 


13.89 


11.45 


13.84 


11.51 


18 




19 


14.77 


11.96 


14.71 


12.02 


14.66 


12.09 


14.61 


12.15 


19 




20 


15.54 


12.59 


15.49 


12.65 


15.43 


12.72 


15.38 


12.79 


20 




21 


16.32 


13.22 


16.26 


13.29 


16.20 


13.36 


16.15 


13.43 


21 




22 


17.10 


13.84 


17.04 


13.92 


16.98 


13.99 


16.91 


14.07 


22 




23 


17.87 


14.47 


17.81 


14.55 


17.75 


14.63 


17.68 


14.71 


23 




24 


18.65 


15.10 


18.59 


15.18 


18.52 


15.27 


18.45 


15.35 


24 




25 


19.43 


15.73 


19.36 


15.82 


19.29 


15.90 


19.22 


15.99 


25 




20 


20.21 


16.36 


20.13 


16.45 


20.06 


16.54 


19.99 


16.63 


26 




27 


20.93 


16.99 


20.91 


17.08 


20.83 


17.17 


20.76 


17.26 


27 




28 


21.76 


17.62 


21.68 


17.72 


21.61 


17.81 


21.53 


17.90 


28 




29 


22.54 


18.25 


22.46 


18.35 


22.38 


18.45 


22.30 


18.54 


29 




30 


23.31 


18.83 


23.23 


18.98 


23.15 


19.08 


23.07 


19.18 


30 




31 


24.09 


19.51 


24.01 


19.61 


23.92 


19.72 


23.83 


19.82 


31 




32 


24.87 


20.14 


24.78 


20.25 


24.69 


20.35 


24.60 


20.46 


32 




33 


25.65 


20.77 


25.55 


20.88 


25.46 


20.99 


25.37 


21.10 


33 




34 


26.42 


21.40 


26.33 


21.51 


26.24 


21.63 


26.14 


21.74 


34 




35 


27.20 


22.03 


27.10 


22.14 


27.01 


22.26 


26.91 


22.38 


35 




36 


27.98 


22.66 


27.88 


22.78 


27.78 


22.90 


27.68 


23.02 


36 




37 


28.75 


23.28 


28.65 


23.41 


28.55 


23.53 


28.45 


23.66 


37 




38 


29.53 


23.91 


29.43 


24.04 


29.32 


24.17 


29.22 


24.30 


38 




39 


30.31 


24.54 


30.20 


24.68 


30.09 


24.81 


29.98 


24.94 


39 




40 


31.09 


25.17 


30.98 


25.31 


30.86 


25.44 


30.75 


25-58 


40 




41 


31.86 


25.80 


31.75 


25.94 


31.64 


26.08 


31.52 


26.22 


41 




42 


32.64 


26.43 


32.52 


26.57 


32.41 


26.72 


32.29 


26.86 


42 




43 


33.42 


27.06 


33.30 


27.21 


33.18 


27.35 


33.06 


27.50 


43 




44 


34.19 


27.69 


34.07 


27.84 


33.95 


27.99 


33.83 


28.14 


44 




45 


34.97 


28.32 


34.85 


28.47 


34.72 


28.62 


34.60 


28.77 


45 




46 


35.75 


28.95 


35.62 


29.10 


35.49 


29.26 


35.37 


29.41 


46 




47 


36.53 


29.58 


36.40 


29.74 


36.27 


29.90 


36.14 


30.05 


47 




48 


37.30 


30.21 


37.17 


30.37 


37.04 


30.53 


36.90 


30.69 


48 




49 


38.08 


30.84 


37.95 


31.00 


37.81 


31.17 


37.67 


31.33 


49 




50 


38.86 


31.47 


38.72 


31.64 


38.58 


31.80 


38.44 


31.97 


50 






Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. | Lat. 


c 

M 

Q 




51 1 


>g- 


50| 


Deg. 


50* Deg. 


50* Deg. 











TF 


.AVER 


3E TA] 


BLE. 






81 


g 

1 

o 

CD 


39 Peg. 


39i Deg. 


39i Deg. 


39} Deg. 


o 

o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


39.63 


32.10 


39.49 


32.27 


39.35 


32.44 


39.21 


32.61 


51 


52 


40.41 


32.72 


40.27 


32.90 


40.12 


33.08 


39.98 


33.25 


52 


53 


41.19 


33.35 


41.04 


33.53 


40.90 


33.71 


40.75 


33.89 


53 


54 


41.97 


33.98 


41.82 


34.17 


41.67 


34.35 


41.52 


34.53 


54 


55 


42.74 


34.61 


42.59 


34.80 


42.44 


34.98 


42.29 


35.17 


55 


56 


43.52 


35.24 


43.37 


35.43 


43.21 


35.62 


43.06 


35.81 


56 


57 


44.30 


35.87 


44.14 


36.06 


43.98 


36.26 


43.82 


36.45 


57 


58 


45.07 


36.50 


44.91 


36.70 


44.75 


36.89 


44.59 


37.09 


58 


59 


45.85 


37.13 


45.69 


37.33 


45.53 


37.53 


45.36 


37.73 


59 


60 


46.63 


37.76 


46.46 


37.96 


46.30 


38.16 


46.13 


38.37 


60 


61 


47.41 


38.39 


47.24 


38.60 


47.07 


38.80 


46.90 


39.01 


61 


62 


48.18 


39.02 


48.01 


39.23 


47.84 


39.44 


47.67 


39.65 


62 


63 


48.96 


39.65 


48.79 


39.86 


48.61 


40.07 


48.44 


40.28 


63 


64 


49.74 


40.28 


49.56 


40.49 


49.38 


40.71 


49.21 


40.92 


64 


65 


50.51 


40.91 


50.34 


41.13 


50.16 


41.35 


49.97 


41.56 


65 


66 


51.29 


41.54 


51.11 


41.76 


50.93 


41.98 


50.74 


42.20 


66 


67 


52.07 


42.16 


51.88 


42.39 


51.70 


42.62 


51.51 


42.84 


67 


68 


52.85 


42.79 


52.66 


43.02 


52.47 


43.25 


52.28 


43.48 


68 


69 


53.52 


43.42 


53.43 


43.66 


53.24 


43.89 


53.05 


44.12 


69 


70 


54.40 


44.05 


54.21 


44.29 


54.01 


44.53 


53.82 


44.76 


70 


71 


55.18 


44.68 


54.98 


44.92 


54.79 


45.16 


54.59 


45.40 


71 


72 


55.95 


45.31 


55.76 


45.55 


55.56 


45.80 


55.36 


46.04 


72 


73 


56.73 


45.94 


56.53 


46.19 


56.33 


4^.43 


56.13 


46.68 


73 


74 


57.51 


46.57 


57.31 


46.82 


57.10 


47.07 


56.89 


47.32 


74 


75 


58.29 


47.20 


58.08 


47.45 


57.87 


47.71 


57.66 


47.96 


75 


76 


59.06 


47.83 


58.85 


48.09 


58.64 


48.34 


58.43 


48.60 


76 


77 


59.84 


48.46 


59.63 


48.72 


59.42 


48.98 


59.20 


49.24 


77 


78 


60.62 


49.09 


60.40 


49.35 


60.19 


49.61 


59.97 


49.88 


78 


79 


61.39 


49.72 


61.18 


49.98 


60.96 


50.25 


60.74 


50.52 


79 


80 


62.17 


50.35 


61.95 


50.62 


61.73 


50.89 


61.51 


51.16 


80 


81 


62.95 


50.97 


62.73 


51.25 


62.50 


51.52 


62.28 


51.79 


81 


82 


63.73 


51.60 


63.50 


51.88 


63.27 


52.16 


63.04 


52.43 


82 


83 


64.50 


52.23 


64.27 


52.51 


64.04 


52.79 


63.81 


53.07 


83 


84 


65.28 


52.86 


65.05 


53.15 


64.82 


53.43 


64.58 


53.71 


84 


85 


66.06 


53.49 


65.82 


53.78 


65.59 


54.07 


65.35 


54.35 


85 


86 


66.83 


54.12 


66.60 


54.41 


66.36 


54.70 


66.12 


54.99 


86 


87 


67.61 


54.75 


67.37 


55.05 


67.13 


55.34 


66.89 


55.63 


87 


88 


68.39 


55.38 


68.15 


55.68 


67.90 


55.97 


67.66 


56.27 


88 


89 


69.17 


56.01 


68.92 


56.32 


68.67 


56.61 


68.43 


56.91 


89 


90 


69.94 


56.64 


69.70 


56.94 


69.45 


57.25 


69.20 


57.55 


90 


91 


70.72 


57.27 


70.47 


57.58 


70.22 


57.88 


69.96 


58.19 


91 


92 


71.50 


57.90 


71.24 


58.21 


70.99 


58.52 


70.73 


58.83 


92 


93 


72.27 


58.53 


72.02 


58.84 


71.76 


59.16 


71.50 


59.47 


93 


94 


73.05 


59.16 


72.79 


59.47 


72.53 


59.79 


72.27 


60.11 


94 


95 


73.83 


59.79 


73.57 


60.11 


73.30 


60.43 


73.04 


60.75 


95 


96 


74.61 


60.41 


74.34 


60.74 


74.08 


61.06 


73.81 


61.39 


96 


97 


75.38 


61.04 


75.12 


61.37 


74.85 


61.70 


74.58 


62.03 


97 


98 


76.16 


61.67 


75.89 


62.01 


75.62 


62.34 


75.35 


62.66 


98 


99 


76.94 


62.30 


76.66 


62.64 


76.39 


62.97 


76.12 


63.30 


99 


100 


77.71 


62.93 


77.44 


63.27 


77.16 


63.61 


76.88 


63.94 


100 


o 
a 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. | Lat. 


4) 

O 

a 
Q 


51 Deg. 


50} Deg. 


50* Deg. 


50i Deg. 



31 



2Z 



82 



TRAVERSE TABLE 



d 
1 

o 

■ 


40 Deg. 


40* Deg. 


40i Deg. 


40J Deg. 


s 
o 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.77 


0.64 


0.76 


0.65 


0.76 


0.65 


0.76 


0.65 


1 


2 


1.53 


1.29 


1.53 


1.29 


1.52 


1.30 


1.52 


1.31 


2 


3 


2.30 


1.93 


2.29 


1.94 


2.28 


1.95 


2.27 


1.96 


3 


> 4 


3.06 


2.57 


3.05 


2.58 


3.04 


2.60 


3.03 


2.61 


4 


! 5 


3.83 


3.21 


3.82 


3.23 


3.80 


3.25 


3.79 


3.26 


5 


6 


4.60 


3.86 


4.58 


3.88 


4.56 


3.90 


4.55 


3.92 


6 


7 


5.36 


4.50 


5.34 


4.52 


5.32 


4.55 


5.30 


4.57 


7 


8 


6.13 


5.14 


6.11 


5.17 


6.08 


5.20 


6.06 


5.22 


8 


9 


6.89 


5.79 


6.87 


5.82 


6.84 


5.84 


6.82 


5.87 


9 


10 


7.66 


6.43 


7.63 


6.46 


7.60 


6.49 


7.58 


6.53 


10 

11 


11 


8.43 


7.07 


8.40 


7.11 


8.36 


7.14 


8.33 


7.18 


12 


9.19 


7.71 


9.16 


7.75 


9.12 


7.79 


9.09 


7.83 


12 


13 


9.96 


8.36 


9.92 


8.40 


9.89 


8.44 


9.85 


8.49 


13 


14 


10.72 


9.00 


10.69 


9.05 


10.65 


9.09 


10.61 


9.14 


14 


15 


11.49 


9.64 


11.45 


9.69 


11.41 


9.74 


11.36 


9.79 


15 


16 


12.26 


10.28 


12.21 


10.34 


12.17 


10.39 


12.12 


10.44 


16 


17 


13.02 


10.93 


12.97 


10.98 


12.93 


11.04 


12.88 


11.10 


17 


18 


13.79 


11.57 


13.74 


11.63 


13.69 


11.69 


13.64 


11.75 


18 


19 


14.55 


12.21 


14.50 


12.28 


14.45 


12.34 


14.39 


12.40 


19 


20 


15.32 


12.86 


15.26 


12.92 


15.21 


12.99 


15.15 


13.06 


20 


21 


16.09 


13.50 


16.03 


13.57 


15.97 


13.64 


15.91 


13.71 


21 


22 


16.85 


14.14 


16.79 


14.21 


16.73 


14.29 


16.67 


14.36 


22 


23 


17.62 


14.78 


17.55 


14.86 


17.49 


14.94 


17.42 


15.01 


23 


24 


18.39 


15.43 


18.32 


15.51 


18.25 


15.59 


18.18 


15.67 


24 


25 


19.15 


16.07 


19.08 


16.15 


19.01 


16.24 


18.94 


16.32 


25 


26 


19.92 


16.71 


19.84 


16.80 


19.77 


16.89 


19.70 


16.97 


26 


27 


20.68 


17.36 


20.61 


17.45 


20.53 


17.54 


20.45 


17.62 


27 


28 


21.45 


18.00 


21.37 


18.09 


21.29 


18.18 


21.21 


18.28 


28 


29 


22.22 


18.64 


22.13 


18.74 


22.05 


18.83 


21.97 


18.93 


29 


30 


22.98 


19.28 


22.90 


19.38 


22.81 


19.48 


22.73 


19.58 


30 


31 


23.75 


19.93 


23.66 


20.03 


23.57 


20.13 


23.48 


20.24 


31 


32 


24.51 


20.57 


24.42 


20.68 


24.33 


20.78 


24.24 


20.89 


32 


33 


25.28 


21.21 


25.19 


21.32 


25.09 


21.43 


25.00 


21.54 


33 


34 


26.05 


21.85 


25.95 


21.97 


25.85 


22.08 


25.76 


22.19 


34 


35 


26.81 


22.50 


26.71 


22.61 


26.61 


22.73 


26.51 


22.85 


35 


36 


27.58 


23.14 


27.48 


23.26 


27.37 


23.38 


27.27 


23.50 


36 


37 


28.34 


23.78 


28.24 


23.91 


28.13 


24.03 


28.03 


24.15 


37 


38 


29.11 


24.43 


29.00 


24.55 


28.90 


24.68 


28.79 


24.80 


38 


39 


29.88 


25.07 


29.77 


25.20 


29.66 


25.33 


29.54 


25.46 


39 


40 


30.64 


25.71 


30.53 


25.84 


30.42 


25.98 


30.30 


26.11 


40 


41 


31.41 


26.35 


31.29 


26.49 


31.18 


26.63 


31.06 


26.76 


41 


42 


32.17 


27.00 


32.06 


27.14 


31.94 


27.28 


31.82 


27 42 


42 


43 


32.94 


27.64 


32.82 


27.78 


32.70 


27.93 


32.58 


2b. 07 


43 


44 


33.71 


28.28 


33.58 


28.43 


33.46 


28.58 


33.33 


28.72 


44 


45 


34.47 


28.93 


34.35 


29.08 


34.22 


29.23 


34.09 


29.37 


45 


46 


35.24 


29.57 


35.11 


29.72 


34.98 


29.87 


34.85 


30.03 


46 


47 


36.00 


30.21 


35.87 


30.37 


35.74 


30.52 


35.61 


30.68 


47 


48 


36.77 


30.85 


36.64 


31.01 


36.50 


31.17 


36.36 


31.33 


4!! 


49 


37.54 


31.50 


37.40 


31.66 


37.26 


31.82 


37.12 


31.99 


49 


50 


38.30 


32.14 


38.16 


32.31 


38.02 


32.47 


37.88 


32.64 


50 


o 

a 

S 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


s 

o 

c 

Q 


50] 


3eg. 


49| Deg. 


49i 


Deg. 


49* Deg. 



TRAVERSE TABLE. 



83 



a 
a 


40 Deg. 


40* Deg. 


40* Deg. 


40$ Deg. 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


39.07 


32.78 


38.92 


32.95 


38.78 


33.12 


38.64 


33.29 


51 


52 


39.83 


33.42 


39.69 


33.60 


39.54 


33.77 


39.39 


33.94 


52 


53 


40.60 


34.07 


40.45 


34.24 


40.30 


34.42 


40.15 


34.60 


53 


54 


41.37 


34.71 


41.21 


34.89 


41.06 


35.07 


40.91 


35.25 


54 


55 


42.13 


35.35 


41.98 


35.54 


41.82 


35.72 


41.67 


35.90 


55 


56 


42.90 


36.00 


42.74 


36.18 


42.58 


36.37 


42.42 


36.55 


56 


57 


43.66 


36.64 


43.50 


36.83 


43.34 


37.02 


43.18 


37.21 


57 


58 


44.43 


37.28 


44.27 


37.48 


44.10 


37.67 


43.94 


37.86 


58 


59 


45.20 


37.92 


45.03 


38.12 


44.86 


38.32 


44.70 


38.51 


59 


60 


45.96 


38.57 


45.79 


38.77 


45.62 


38.97 


45.45 


39.17 


60 


61 


46.73 


39.21 


46.56 


39.41 


46.38 


39.62 


46.21 


39.82 


61 


62 


47.49 


39.85 


47.32 


40.06 


47.15 


40.27 


46.97 


40.47 


62 


63 


48.26 


40.50 


48.08 


40.71 


47.91 


40.92 


47.73 


41.12 


63 


64 


49.03 


41.14 


48.85 


41.35 


48.67 


41.56 


48.48 


41.78 


64 


65 


49.79 


41.78 


49.61 


42.00 


49.43 


42.21 


49.24 


42.43 


65 


66 


50.56 


42.42 


50.37 


42.64 


50.19 


42.86 


50.00 


43.08 


66 


67 


51.32 


43.07 


51.14 


43.29 


50.95 


43.51 


50.76 


43.73 


67 


68 


52.09 


43.71 


51.90 


43.94 


51.71 


44.16 


51.51 


44.39 


68 


69 


52.86 


44.35 


52.66 


44.58 


52.47 


44.81 


52.27 


45.04 


69 


70 


53.62 


45.00 


53.43 


45.23 


53.23 


45.46 


53.03 


45.69 


70 


71 


54.39 


45.64 


54.19 


45.87 


53.99 


46.11 


63.79 


46.35 


71 


72 


55.16 


46.28 


54.95 


46.52 


54.75 


46.76 


54.54 


47.00 


72 


73 


55.92 


46.92 


55.72 


47.17 


55.51 


47.41 


55.30 


47.65 


73 


74 


56.69 


47.57 


56.48 


47.81 


56.27 


48.06 


56.06 


48.30 


74 


75 


57.45 


48.21 


57.24 


48.46 


57.03 


48.71 


56.82 


48.96 


75 


76 


58.22 


48.85 


58.01 


49.11 


57.79 


49.36 


57.57 


49.61 


76 


77 


58.99 


49.49 


58.77 


49.75 


58.55 


50.01 


58.33 


50.26 


77 


78 


59.75 


50.14 


59.53 


50.40 


59.31 


50.66 


59.09 


50.92 


78 


79 


60.52 


50.78 


60.30 


51.04 


60.07 


51.31 


59.85 


51.57 


79 


80 


61.28 


51.42 


61.06 


51.69 


60.83 


51.96 


60.61 


52.22 


80 


81 


62.05 


52.07 


61.82 


52.34 


61.59 


52.61 


61.36 


52.87 


81 


82 


62.82 


52.71 


62.59 


52.98 


62.35 


53.25 


62.12 


53.53 


82 


83 


63.58 


53.35 


63.35 


53.63 


63.11 


53.90 


62.88 


54.18 


83 


84 


64.35 


53.99 


64.11 


54.27 


63.87 


54.55 


63.64 


54.83 


84 


85 


65.11 


54.64 


64.87 


54.92 


64.63 


55.20 


64.39 


55.48 


85 


86 


65.88 


55.28 


65.64 


55.57 


65.39 


55.85 


65.15 


56.14 


86 


87 


66.65 


55.92 


66.40 


56.21 


66.16 


56.50 


65.91 


56.79 


87 


88 


67.41 


56.57 


67.16 


56.86 


66.92 


57.15 


66.67 


57.44 


88 


89 


68.18 


57.21 


67.93 


57.50 


67.68 


57.80 


67.42 


58.10 


89 


90 


68.94 


57.85 


68.69 


58.15 


68.44 


58.45 


68.18 


58.75 


90 


91 


69.71 


58.49 


69.45 


58.80 


69.20 


59.10 


68.94 


59.40 


91 


92 


70.48 


59.14 


70.22 


59.44 


69.96 


59.75 


69.70 


60.05 


92 


93 


71.24 


59.78 


70.98 


60.09 


70.72 


60.40 


70.45 


60.71 


93 


94 


72.01 


60.42 


71.74 


60.74 


71.48 


61.05 


71.21 


62.36 


94 


95 


72.77 


61.06 


72.51 


61.38 


72.24 


61.70 


71.97 


62.01 


95 


96 


73.54 


61.71 


73.27 


62.03 


73.00 


62.35 


72.73 


62.66 


96 


97 


74.31 


62.35 


74.03 


62.67 


73.76 


63.00 


73.48 


63.32 


97 


98 


75.07 


62.99 


74.80 


63.32 


74.52 


63. 65 


74.24 


63.97 


98 


99 


75.84 


63.64 


75.56 


63.97 


75.28 


64.30 


75.00 


64.62 


99 


100 


76.60 


64.28 


76.32 


64.61 


76.04 


64.94 


75.76 


65.28 


100 


1 

s 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


m 

o 
a 

■s 

Q 


50 Deg. 


49} Deg. 


49£ Deg. 


49i Deg. 



84 



TRAVERSE TABLE. 



o 

O 
? 


41 Deg. 


41J Deg. 


41 i Deg. 


41} Deg. 


! 

? 




Lat. 


Dep. 


Lat 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




1 


0.75 


0.66 


0.75 


0.66 


0.75 


0.66 


0.75 


0.67 


1 




2 


1.51 


1.31 


1.50 


1.32 


1.50 


1.33 


1.49 


1.33 


2 




3 


2.26 


1.97 


2.26 


1.98 


2.25 


1.99 


2.24 


2.00 


3 




4 


3.02 


2.62 


3.01 


2.64 


3.00 


2.65 


2.98 


2.66 


4 




5 


3.77 


3.28 


3.76 


3.30 


3.74 


3.31 


3.73 


3.33 


5 




6 


4.53 


3.94 


4.51 


3.96 


4.49 


3.98 


4.48 


4.00 


6 




7 


5.28 


4.59 


5.26 


4.62 


5.24 


4.64 


5.22 


4.66 


7 




8 


6.04 


5.25 


6.01 


5.27 


5.99 


5.30 


5.97 


5.33 


8 




9 


6.79 


5.90 


6.77 


5.93 


6.74 


5.96 


6.71 


5.99 


9 




10 


7.55 


6.56 


7.52 


6.59 


7.49 


6.63 


7.46 


6.66 


10 




11 


8.30 


7.22 


8.27 


7.25 


8.24 


7.29 


8.21 


7.32 


11 




12 


9.06 


7.87 


9.02 


7.91 


8.99 


7.95 


8.95 


7.99 


12 




13 


9.81 


8.53 


9.77 


8.57 


9.74 


8.61 


9.70 


8.66 


13 




14 


10.57 


9.18 


10.53 


9.23 


10.49 


9.28 


10.44 


9.32 


14 




15 


11.32 


9.84 


11.28 


9.89 


11.23 


9.94 


11.19 


9.99 


15 




16 


12.08 


10.50 


12.03 


10.55 


11.98 


10.60 


11.94 


10.65 


16 




17 


12.83 


11.15 


12.78 


11.21 


12.73 


11.26 


12.68 


11.32 


17 




18 


13.58 


11.81 


13.53 


11.87 


13.48 


11.93 


13.43 


11.99 


18 




19 


14.34 


12.47 


14.28 


12.53 


14.23 


12.59 


14.18 


12.65 


19 




20 


15.09 


13.12 


15.04 


13.19 


14.98 


13.25 


14.92 


13.32 


20 




21 


15.85 


13.78 


15.79 


13.85 


15.73 


13.91 


15.67 


13.98 


21 




22 


16.60 


14.43 


16.54 


14.51 


16.48 


14.58 


16.41 


14.65 


22 




23 


17.36 


15.09 


17.29 


15.16 


17.23 


15.24 


17.16 


15.32 


23 




24 


18.11 


15.75 


18-04 


15.82 


17.97 


15.90 


17.91 


15.98 


24 




25 


18.87 


16.40 


18.80 


16.48 


18.72 


16.57 


13.65 


16.65 


25 




26 


19.62 


17.06 


19.55 


17.14 


19.47 


17.23 


19.40 


17.31 


26 




27 


20.38 


17.71 


20.30 


17.80 


20.22 


17.89 


20.14 


17.98 


27 




28 


21.13 


18.37 


21.05 


18.46 


20.97 


18.55 


20.89 


18.64 


28 




29 


21.89 


19.03 


21.80 


19.12 


21.72 


19.22 


21.64 


19.31 


29 




30 


22.64 


19.68 


22.56 


19.78 


22.47 


19.88 


22.38 


19.98 


30 




31 


23.40 


20.34 


23.31 


20.44 


23.22 


20.54 


23.13 


20.64 


31 




32 


24.15 


20.99 


24.06 


21.10 


23-97 


21.20 


23.87 


21.31 


32 




33 


24.91 


21.65 


24.81 


21.76 


24.72 


21.87 


24.62 


21.97 


33 




34 


25.66 


22.31 


25.56 


22.42 


25.46 


22.53 


25.37 


22.64 


34 




35 


26.41 


22.96 


26.31 


23.08 


26.21 


23.19 


26.11 


23.31 


35 




36 


27.17 


23.62 


27.07 


23.74 


26.96 


23.85 


26.86 


23.97 


36 




37 


27.92 


24.27 


27.82 


24.40 


27.71 


24.52 


27.60 


24.64 


37 




38 


28.68 


24.93 


28.57 


25.06 


28.46 


25.18 


28.35 


25.30 


38 




39 


29.43 


25.59 


29.32 


25.71 


29.21 


25 .84 


29.10 


25.97 


30 




40 


30.19 


26.24 


30.07 


26.37 


29.96 


26.50 


29.84 


26.64 


40 




41 


30.94 


26.90 


30.83 


27.03 


30.71 


27.17 


30.59 


27.30 


41 




42 


31.70 


27.55 


31.58 


27.69 


31.46 


27.83 


31.33 


27.97 


42 




43 


32.45 


28.21 


32.33 


28.35 


32.21 


28.49 


32.08 


28.63 


43 




44 


33.21 


28.87 


33.08 


29.01 


32.95 


29.16 


32.83 


29.30 


44 




45 


33.96 


29.52 


33.83 


29.67 


33.70 


29.82 


33.57 


29.97 


45 




46 


34.72 


30.18 


34.58 


30.33 


34.45 


30.48 


34.32 


30.63 


46 




47 


35.47 


30.83 


35.34 


30.99 


35.20 


31.14 


35.06 


31.30 


47 




48 


36.23 


31.49 


36.09 


31.65 


35.95 


31.81 


35.81 


31.96 


48 




49 


36.98 


32.15 


36.84 


32.31 


36.70 


32.47 


36.56 


32.63 


49 1 




50 


37.74 


32.80 


37.59 


32.97 


?~.45 


33.13 


37.30 


33.29 


50 '• 




o 
1 = 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


o 




40 [ 


•eg. 

1 


48} 


Deg. 


48i 


00, 


4-84 


Deg. 


1 



TRAVERSE TABLE 



35 



g 

D 
O 
(0 


41 Deg. 


41} 


Deg. 


41J Deg. 


41| Deg. 


O 

w 
s 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


38.49 


33.46 


38.34 


33.63 


38.20 


33.79 


38.05 


33.96 


51 


52 


39.24 


34.12 


39.10 


34.29 


38.95 


34.46 


38.79 


34.63 


52 


53 


40.00 


34.77 


39.85 


34.95 


39.69 


35.12 


39.54 


35.29 


53 


54 


40.75 


35.43 


40.60 


35.60 


40.44 


35.78 


40.29 


! 35.96 


54 


55 


41.51 


36.08 


41.35 


36.26 


41.19 


36.44 


41.03 


36.62 


55 


56 


42.26 ' 36.74 


42.10 


36.92 


41.94 


37.11 


41.78 


37.29 


56 


57 


43.02 37.40 


42.85 


37.58 


42.69 


37.77 


42.53 


37.96 


57 


58 


43.77 


38.05 


43.61 


38.24 


43.44 


38.43 


43.27 


38.62 


58 


59 


44.53 


38.71 


44.36 


38.90 


44.19 


39.09 


44.02 


39.29 


59 


60 


45.28 


39.36 


45.11 


39.56 


44.94 


39.76 


44.76 


39.95 


60 


61 


46.04 


40.02 


45.86 


40.22 


45.69 


40.42 


45.51 


40.62 


61 


62 


46.79 


40.68 


46.61 


40.88 


46.44 


41.08 


46.26 


41.28 


62 


63 


47.55 


41.33 


47.37 


41.54 


47.18 


41.75 


47.00 


41.95 


63 


64 


48.30 


41.99 


48.12 


42.20 


47.93 


42.41 


47.75 


42.62 


64 


65 


49.06 


42.64 


48.87 


42.86 


48.68 


43.07 


48.49 


43.28 


65 ; 


66 


49.81 


43.30 


49.62 


43.52 


49.43 


43.73 


49.24 


43.95 


66 


67 


50.57 


43.96 


50.37 


44.18 


50.18 


44.40 


49.99 


44.61 


67 


68 


51.32 


44.61 


51.13 


44.84 


50.93 


45.06 


50.73 


45.28 


68 


69 


52.07 


45.27 


51.88 


45.49 


51.68 


45.72 


51.48 


45.95 


69 


70 


52.83 


45.92 


52.63 


46.15 


52.43 


46.38 


52.22 


46.61 


70 


71 


53.58 


46.58 


53.38 


46.81 


53.18 


47.05 


52.97 


47.28 


71 


72 


54.34 


47.24 


54.13 


47.47 


53.92 


47.71 


53.72 


47.94 


72 


73 


55.09 


47.89 


54.88 


43.13 


54.67 


48.37 


54.46 


48.61 


73 


74 


55.85 


48.55 


55.64 


48.79 


55.42 


49.03 


55.21 


49.28 


74 


75 


56.60 


49.20 


56.39 


49.45 


56.17 


49.70 


55.95 


49.94 


75 


76 


57.36 


49.86 


57.14 


50.11 


56 .92 


50.36 


56.70 


50.61 


76 


77 


58.11 


50.52 


57.89 


50.77 


57.67 


51.02 


57.45 


51.27 


77 


78 


58.87 


51.17 


58.64 


51.43 


58.42 


51.68 


58.19 


51.94 


78 


79 


59.62 


51.83 


59.40 


52.09 


59.17 


52.35 


58.94 


52.60 


79 


80 


60.38 


52.48 


60.15 


52.75 


59.92 


53.01 


59.68 


53.27 


80 


81 


61.13 


53.14 


60.90 


53.41 


60.67 


53.67 


60.43 


53.94 


81 


82 


61.89 


53.80 


61.65 


54.07 


61.41 


54.33 


61.18 


54.60 


82 


83 


62.64 


54.45 


62.40 


54.73 


62.16 


55.00 


61.92 


55.27 


83 


84 


63.40 


55.11 


63.15 


55.33 


62.91 


55.66 


62.67 


55.93 


84 ' 


85 


64.15 


55.76 


63.91 


56.04 


63.66 


56.32 


63.41 


56.60 


85 


86 


64.90 


56.42 


64.66 


56.70 


64.41 


56.99 


64.16 


57.27 


86 


87 


65.66 


57.08 


65.41 


57.36 


65.16 


57.65 


64.91 


57.93 


87 


88 


66.41 


57.73 


66.16 


58.02 


65.91 


58.31 


65.65 


58.60 


88 ! 


89 


67.17 


58.39 


66.91 


58.68 


66.66 


58.97 


66.40 


59.26 


89 • 


90 


67.92 


59.05 


67.67 


59.34 


67.41 


59.64 


67.15 


59.93 


90 


91 


68.68 


59.70 


68.42 


60.00 


68.15 


60.30 


67.89 


60.60 


91 


92 


69.43 


60.36 


69.17 


60.66 


68.90 


60.96 


68.64 


61.26 


92 i 


93 


70.19 


61.01 


69.92 


61.32 


69.65 


61.62 


69.38 


61.93 


93 


94 


70.94 


61.67 


70.67 


61.98 


70.40 


62.29 


70.13 


62.59 


94 J 


95 


71.70 


62.33 


71.43 


62.64 


71.15 


62.95 


70.88 


63.26 


95 . 


! 96 


72.45 


62.98 


72.18 


63.30 


71.90 


63.61 


71.62 


63.92 


96 


' 97 


73.21 


63.64 


72.93 


63.96 


72.65 


64.27 


72.37 


64.59 


97 


I 98 


73.96 


64.29 


73.68 


64.62 


73.40 


64.94 


73.11 


65.26 


98 


99 


74.72 


64.95 


74.43 


65.28 


74.15 


65.60 


73.86 


65.92 


99 


100 


75.47 


65.61 


75.18 


65.93 


74.90 


66.26 


74.61 


66.59 


100 


a! 

1 -2 


.Jep. 


Lat 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


9 

s 

e 

£ 


4^ 


i 
Oeg. - 


48| 


Deg. 


48i 


Deg. 


48} 


Deg. 



86 



TRAVERSE TABLE. 





3 
O 

5 


42 Deg. 


42* Deg. 


42J Deg. 


42* Deg. 


1 
o 






Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 






1 


0.74 


0.67 


0.74 


0.67 


0.74 


0.68 


0.73 


0.68 


1 






2 


1.49 


1.34 


1.48 


1.34 


1.47 


1.35 


1.47 


1.36 


2 






3 


2.23 


2.01 


2.22 


2.02 


2.21 


2.03 


2.20 


2.04 


3 






4 


2.97 


2.68 


2.96 


2.69 


2.95 


2.70 


2.94 


2.72 


4 






5 


3.72 


3.35 


3.70 


3.36 


3.69 


3.38 


3.67 


3.39 


5 






6 


4.46 


4.01 


4.44 


4.03 


4.42 


4.05 


4.41 


4.07 


6 






7 


5.20 


4.68 


5.18 


4.71 


5.16 


4.73 


5.14 


4,75 


7 






8 


5.95 


5.35 


5.92 


5.38 


5.90 


5.40 


5.87 


5.43 


8 






9 


6.69 


6.02 


6.66 


6.05 


6.64 


6.08 


6.61 


6.11 


9 






10 


7.43 


6.69 


7.40 


6.72 


7.37 


6.76 


7.34 


6.79 


10 






11 


8.17 


7.36 


8.14 


7.40 


8.11 


7.43 


8.08 


7.47 


11 






12 


8.92 


8.03 


8.88 


8.07 


8.85 


8.11 


8.81 


8.15 


12 






13 


9.66 


8.70 


9.62 


8.74 


9.58 


8.78 


9.55 


8.82 


13 






14 


10.40 


9.37 


10.36 


9.41 


10.32 


9.46 


10.28 


9.50 


14 






15 


11.15 


10.04 


11.10 


10.09 


11.06 


10.13 


11.01 


10.18 


15 






16 


11.89 


10.71 


11.84 


10.76 


11.80 


10.81 


11.75 


10.86 


16 






17 


12.63 


11.38 


12.58 


11.43 


12.53 


11.48 


12.48 


11.54 


17 






18 


13.38 


12.04 


13.32 


12.10 


13.27 


12.16 


13.22 


12.22 


18 






19 


14.12 


12.71 


14.06 


12.77 


14.01 


12.84 


13.95 


12.90 


19 






20 


14.86 


13.38 


14.80 


13.45 


14.75 


13.51 


14.69 


13.58 


20 






21 


15.61 


14.05 


15.54 


14.12 


15.48 


14.19 


15.42 


14.25 


21 






22 


16.35 


14.72 


16.28 


14.79 


16.22 


14.86 


16.16 


14.93 


22 






23 


17.09 


15.39 


17.02 


15.46 


16.96 


15.54 


16.89 


15.61 


23 






24 


17.84 


16.06 


17.77 


16.14 


17.69 


16.21 


17.62 


16.29 


24 






25 


18.58 


16.73 


18.51 


16.81 


18.43 


16.89 


18.36 


16.97 


25 






26 


19.32 


17.40 


19.25 


17.48 


19.17 


17.57 


19.09 


17.65 


26 






27 


20.06 


18.07 


19.99 


18.15 


19.91 


18.24 


19.83 


18.33 


27 






28 


20.81 


18.74 


20.73 


18.83 


20.64 


18.92 


20.56 


19.01 


28 






29 


21.55 


19.40 


21.47 


19.50 


21.38 


19.59 


21.30 


19.69 


29 






30 


22.29 


20.07 


22.21 


20.17 


22.12 


20.27 


22.03 


20.36 


30 






31 


23.04 


20.74 


22.95 


20.84 


22.86 


20.94 


22.76 


21.04 


31 






32 


23.78 


21.41 


23.69 


21.52 


23.59 


21.62 


23.50 


21.72 


32 






33 


24.52 


22.08 


24.43 


22.19 


24.33 


22.29 


24.23 


22.40 


33 






34 


25.27 


22.75 


25.17 


22.86 


25.07 


22.97 


24.97 


23.08 


34 






35 


26.01 


23.42 


25.91 


23.53 


25.80 


23.65 


25.70 


23.76 


35 






36 


26.75 


24.09 


26.65 


24.21 


26.54 


24.32 


26.44 


24.44 


36 






37 


27.50 


24.76 


27.39 


24.83 


27.28 


25.00 


27.17 


25.12 


37 






38 


28.24 


25.43 


28.13 


25.55 


28.02 


25.67 


27.90 


25.79 


38 






39 


28.98 


26.10 


28.87 


26.22 


28.75 


26.35 


28.64 


26.47 


39 






40 


29.73 


26.77 


29.61 


26.89 


29.49 


27.02 


29.37 


27.15 


40 






41 


30.47 


27.43 


30.35 


27.57 


30.23 


27.70 


30.11 


27.83 


41 






42 


31.21 


28.10 


31.09 


28.24 


30.97 


28.37 


30.84 


28.51 


42 






43 


31.96 


28.77 


31.83 


28.91 


31.70 


29.05 


31.58 


29.19 


43 






44 


32.70 


29.44 


32.57 


29.58 


32.44 


29.73 


32.31 


29.87 


44 






45 


33.44 


30.11 


33.31 


30.26 


33.18 


30.40 


33.04 


30.55 


45 






46 


34.18 


30.78 


34.05 


30.93 


33.91 


31.08 


33.78 


31.22 


46 






47 


34.93 


31.45 


34.79 


31.60 


34.65 


31.75 


34.51 


31.90 


47 






48 


35.67 


32.12 


35.53 


32.27 


35.39 


32.43 


35.25 


32.58 


48 






49 


36.41 


32.79 


36.27 


32.95 


36.13 


33.10 


35.98 


33.26 


49 






50 


37.16 


33.46 


37.01 


33.62 


36.86 


33.78 


36.72 


33.94 


50 






3 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. I Lat 


i 

c 

b 






48 Deg-. 


47} Deg. 


47* Deg. 


47i Deg. 





TRAVERSE TABLE. 



87 



f 

a 
a 
? 


42 Deg. 


42i Deg. 


42J Deg. 


42| Deg. 


g 

1 
o 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


37.90 


34.13 


37.75 


34.29 


37.60 


34.46 


37.45 


34.62 


51 


52 


38.64 


34.79 


38.49 


34.96 


38.34 


35.13 


38.18 


35.30 


52 


53 


39.39 


35.46 


39.23 


35.64 


39.08 


35.81 


38.92 


35.98 


53 


54 


40.13 


36.13 


39.97 


36.31 


39.81 


36.48 


39.65 


36.66 


54 


55 


40.87 


36.80 


40.71 


36.98 


40.55 


37.16 


40.39 


37.33 


55 


56 


41.62 


37.47 


41.45 


37.65 


41.29 


37.83 


41.12 


38.01 


56 


57 


42.36 


38.14 


42.19 


38.32 


42.02 


38.51 


41.86 


38.69 


57 


58 


43.10 


38.81 


42.93 


39.00 


42.76 


39.18 


42.59 


39.37 


58 


59 


43.85 


39.48 


43.67 


39.67 


43.50 


39.86 


43.32 


40.05 


59 


60 


44.59 


40.15 


44.41 


40.34 


44.24 


40.54 


44.06 


40.73 


60 


61 


45.33 


40.82 


45.15 


41.01 


44.97 


41.21 


44.79 


41.41 


61 


62 


46.07 


41.49 


45.89 


41.69 


45.71 


41.89 


45.53 


42.09 


62 


63 


46.82 


42.16 


46.63 


42.36 


46.45 


42.56 


46.26 


42.76 


63 


64 


47.56 


42.82 


47.37 


43.03 


47.19 


43.24 


47.00 


43.44 


64 


65 


48.30 


43.49 


48.11 


43.70 


47.92 


43.91 


47.73 


44.12 


65 


66 


49.05 


44.16 


48.85 


44.38 


48.66 


44.59 


48.47 


44.80 


66 


67 


49.79 


44.83 


49.59 


45.05 


49.40 


45.26 


49.20 


45.48 


67 


68 


50.53 


45.50 


50.33 


45.72 


50.13 


45.94 


49.93 


46.16 


68 


69 


51.28 


46.17 


51.07 


46.39 


50.87 


46.62 


50.67 


46.84 


69 


70 


52.02 


46.84 


51.82 


47.07 


51.61 


47.29 


51.40 


47.52 


70 


71 


52.76 


47.51 


52.56 


47.74 


52.35 


47.97 


52.14 


48.19 


71 


72 


53.51 


48.18 


53.30 


48.41 


53.03 


48.64 


52.87 


48.87 


72 


73 


54.25 


48.85 


54.04 


49.08 


53.82 


49.32 


53.61 


49.55 


73 


74 


54.99 


49.52 


54.78 


49.76 


54.56 


49.99 


54.34 


50.23 


74 


75 


55.74 


50.18 


55.52 


50.43 


55.30 


50.67 


55.07 


50.91 


75 


76 


56.48 


50.85 


56.26 


51.10 


56.03 


51.34 


55.81 


51.59 


76 


77 


57.22 


51.52 


57.00 


51.77 


56.77 


52.02 


56.54 


52.27 


77 


78 


57.97 


52.19 


57.74 


52.44 


57.51 


52.70 


57.28 


52.95 


78 


79 


58.71 


52.86 


58.48 


53.12 


58.24 


53.37 


58.01 


53.63 


79 


80 


59.45 


53.53 


59.22 


53.79 


58.98 


54.05 


58.75 


54.30 


80 


81 


60.19 


54.20 


59.96 


54.46 


59.72 


54.72 


59.48 


54.98 


81 


82 


60.94 


54.87 


60.70 


55.13 


60.46 


55.40 


60.21 


55.66 


82 


83 


61.68 


55.54 


61.44 


55.81 


61.19 


56.07 


60.95 


56.34 


83 


84 


62.42 


56.21 


62.18 


56.48 


61.93 


56.75 


61.68 


57.02 


84 


85 


63.17 


56.88 


62.92 


57.15 


62.67 


57.43 


62.42 


57.70 


85 


86 


63.91 


57.55 


63.66 


57.82 


63.41 


58.10 


63.15 


58.38 


86 


87 


64.65 


58.21 


64.40 


58.50 


64.14 


58.78 


63.89 


59.06 


87 


88 


65.40 


58.88 


65.14 


59.17 


64.88 


59.45 


64.62 


59.73 


88 


89 


66.14 


59.55 


65.88 


59.84 


65.62 


60.13 


65.35 


60.41 


89 


90 


66.88 


60.22 


66.62 


60.51 


66.35 


60.80 


66.09 


61.09 


90 


91 


67.63 


60.89 


67.36 


61.19 


67.09 


61.48 


66.82 


61.77 


91 


92 


68.37 


61.56 


68.10 


61.86 


67.83 


62.15 


67.56 


62.45 


92 


93 


69.11 


62.23 


68.84 


62.53 


68.57 


62.83 


68.29 


63.13 


93 


94 


69.86 


62.90 


69.58 


63.20 


69.30 


63.51 


69.03 


63.81 


94 


95 


70.60 


63.57 


70.32 


63.87 


70.04 


64.18 


69.76 


64.49 


95 


96 


71.34 


64.24 


71.06 


64.55 


70.78 


64.86 


70.49 


65.16 


96 


97 


72.08 


64.91 


71.80 


65.22 


71.52 


65.53 


71.23 


65.84 


97 


98 


72.83 


65.57 


72.54 


65.89 


72.25 


66.21 


71.96 


66.52 


98 


99 


73.57 


66.24 


73.28 


66.56 


72.99 


66.88 


72.70 


67.20 


99 


100 


74.31 


66.91 


74.02 


67.24 


73.73 


67.56 


73.43 


67.88 


100 


o 
a 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


c 

s 


48 I 


>g. 


47| 


Deg. 


47* Deg. 


47i Deg. 



88 



TRAVERSE TABLE. 




& 

3 
o 
9 


43 Deg. 


43i Deg. 


43J Deg. 


43} Deg. 


q 

ST 

s 
o 
n 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.73 


0.68 


0.73 


0.69 


0.73 


0.69 


0.72 


0.69 


1 


2 


1.46 


1.36 


1.46 


1.37 


1.45 


1.38 


1.44 


1.38 


2 


3 


2.19 


2.05 


2.19 


2.06 


2.18 


2.07 


2.17 


2.07 


3 


4 


2.93 


2.73 


2.91 


2.74 


2.90 


2.75 


2.89 


2.77 


4 


5 


3.66 


3.41 


3.64 


3.43 


3.63 


3.44 


3.61 


3.46 


5 


6 


4.39 


4.09 


4.37 


4.11 


4.35 


4.13 


4.33 


4.15 


6 


7 


5.12 


4.77 


5.10 


4.80 


5.08 


4.82 


5.06 


4.84 


7 


8 


5.85 


5.46 


5.83 


5.48 


5.80 


5.51 


5.78 


5.53 


8 


9 


6.58 


6.14 


6.56 


6.17 


6.53 


6.20 


6.50 


6.22 


9 


10 


7.31 


6.82 


7.28 


6.85 


7.25 


6.88 


7.22 


6.92 


10 


11 


8.04 


7.50 


8.01 


7.54 


7.98 


7.57 


7.95 


7.61 


11 


12 


8.78 


8.18 


8.74 


8.22 


8.70 


8.26 


8.67 


8.30 


12 


13 


9.51 


8.87 


9.47 


8.91 


9.43 


8.95 


9.39 


8.99 


13 


14 


10.24 


9.55 


10.20 


9.59 


10.16 


9.64 


10.11 


9.68 


14 


15 


10.97 


10.23 


10.93 


10.28 


10.88 


10.33 


10.84 


10.37 


15 


16 


11.70 


10.91 


11.65 


10.96 


11.61 


11.01 


11.56 


11.06 


16 


17 


12.43 


11.59 


12.38 


11.65 


12.33 


11.70 


12.28 


11.76 


17 


18 


13.16 


12.28 


13.11 


12.33 


13.06 


12.39 


13.00 


12.45 


18 


19 


13.90 


12.96 


13.84 


13.02 


13.78 


13.08 


13.72 


13.14 


19 


20 


14.63 


13.64 


14.57 


13.70 


14.51 


13.77 


14.45 


13.83 


20 


21 


15.36 


14.32 


15.30 


14.39 


15.23 


14.46 


15.17 


14.52 


21 


22 


16.09 


15.00 


16.02 


15.07 


15.96 


15.14 


15.89 


15.21 


22 


23 


16.82 


15.69 


16.75 


15.76 


16.68 


15.83 


16.61 


15.90 


23 


24 


17.55 


16.37 


17.48 


16.44 


17.41 


16.52 


17.34 


16.60 


24 


25 


18.23 


17.05 


18.21 


17.13 


18.13 


17.21 


18.06 


17.29 


25 


26 


19.02 


17.73 


18.94 


17.81 


18.86 


17.90 


18.78 


17.98 


26 


27 


19.75 


18.41 


19.67 


18.50 


19.59 


18.59 


19.50 


18.67 


27 


28 


20.48 


19.10 


20.39 


19.19 


20.31 


19.27 


20.23 


19.36 


28 


29 


21.21 


19.78 


21.12 


19.87 


21.04 


19.96 


20.95 


20.05 


29 


30 


21.94 


20.46 


21.85 


20.56 


21.76 


20.65 


21.67 


20.75 


30 


31 


22.67 


21.14 


22.58 


21.24 


22.49 


21.34 


22.39 


21.44 


31 


32 


23.40 


21.82 


23.31 


21.93 


23.21 


22.03 


23.12 


22.13 


32 


33 


24.13 


22.51 


24.04 


22.61 


23.94 


22.72 


23.84 


22.82 


33 


34 


24.87 


23.19 


24.76 


23.30 


24.66 


23.40 


24.56 


23.51 


34 


35 


25.60 


23.87 


25.49 


23.98 


25.39 


24.09 


25.28 


24.20 


35 


36 


26.33 


24.55 


26.22 


24.67 


26.11 


24.78 


26.01 


24.89 


36 


37 


27.06 


25.23 


26.95 


25.35 


26.84 


25.47 


26.73 


25.59 


37 


38 


27.79 


25.92 


27.68 


26.04 


27.56 


26.16 


27.45 


26.28 


38 


39 


28.52 


26.60 


28.41 


26.72 


28.29 


26.85 


28.17 


26.97 


39 


40 


29.25 


27.28 


29.13 


27.41 


29.01 


27.53 


28.89 


27.66 


40 


41 


29.99 


27.96 


29.86 


28.09 


29.74 


28.22 


29.62 


28.35 


41 


42 


30.72 


28.64 


30.59 


28.78 


30.47 


28.91 


30.34 


29.04 


42 


43 


31.45 


29.33 


31.32 


29.46 


31.19 


29.60 


31.06 


29.74 


43 


44 


32.18 


30.01 


32.05 


30.15 


31.92 


30.29 


31.78 


30.43 


44 


45 


32.91 


30.69 


32.78 


30.83 


32.64 


30.98 


32.51 


31.12 


45 


46 


33.64 


31.37 


33.51 


31.52 


33.37 


31.66 


33.23 


31.81 


46 


47 


34.37 


32.05 


34.23 


32.20 


34.09 


32.35 


33.95 


32.50 


47 


48 


35.10 


32.74 


34.96 


32.89 


34.82 


33.04 


34.67 


33.19 


48 


49 


35.84 


33.42 


35.69 


33.57 


35.54 


33.73 


35.40 


33.88 


49 


50 


36.57 


34.10 


36.42 


34.26 


36.27 


34.42 { 


36.12 


34.58 


50 


c 
a 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


09 

c 
Q : 


47 1 


)eg. 


46$ Deg. 


464 Deg. 


464 


De ? . 



TRAVERSE TABLE. 



89 



o 

o 
to 


43 Deg. 


43* Deg. 


43h 


Jeg. 


43| Deg. 


e 

3 
O 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


37.30 


34.78 


37.15 


34.94 


36.99 


35.11 


36.84 


35.27 


51 


52 


33.03 


35.46 


37.88 


35.63 


37.72 


35.79 


37.56 


35.96 


52 


1 53 


38.76 


36.15 


38.60 


36.31 


38.44 


36.48 


38.29 


36.65 


S3 


i 54 


39.49 


36.83 


39.33 


37.00 


39.17 


37.17 


39.01 


37.34 


54 


55 


40.22 


37.51 


40.06 


37.69 


39.90 


37.86 


39.73 


38.03 


55 


; 53 


40.96 


38.19 


40.79 


38.37 


40.62 


38.55 


40.45 


38.72 


56 ' 


I 57 


41.69 


38.87 


41.52 


39.06 


41.35 


39.24 


41.17 


39.42 


57 


58 


42.42 


39.56 


42.25 


39.74 


42.07 


39.92 


41.90 


40.11 


58 


! 59 


43.15 


40.24 


42.97 


40.43 


42.80 


40.61 


42.62 


40.80 


59 


1 60 


43.88 


40.92 


43.70 


41.11 


43.52 


41.30 


43.34 


41.49 


60 


61 


44.61 


41.60 


44.43 


41.80 


44.25 


41.99 


44.06 


42.18 


61 


62 


45.34 42.28 


45.16 


42.48 


44.97 


42.68 


44.79 


42.87 


62 


63 


46.08 42.97 


45.89 


43.17 


45.70 


43.37 


45.51 


43.57 


63 


64 


46.81 


43.65 


46.62 


43.85 


46.42 


44.05 


46.23 


44.26 


64 


65 


47.54 


44.33 


47.34 


44.54 


47.15 


44.74 


46.95 


44.95 


65 


66 


48.27 


45.01 


48.07 


45.22 


47.87 


45.43 


47.68 


45.64 


66 


67 


49.00 


45.69 


48.80 


45.91 


48.60 


46.12 


48.40 


46.33 


67 


68 


49.73 


46.38 


49.53 


46.59 


49.33 


46.81 


49.12 


47.02 


68 


69 


50.46 


47.06 


50.26 


47.28 


50.05 


47.50 


49.84 


47.71 


69 


70 


51.19 


47.74 


50.99 


47.96 


50.78 


48.18 


50.57 


48.41 


70 


71 51.93 


48.42 


51.71 


48.65 


51.50 


48.87 


51.29 


49.10 


71 


72 


52.66 


49.10 


52.44 


49.33 


52.23 


49.56 


52.01 


49.79 


72 


73 


53.39 


49.79 


53.17 


50.02 


52.95 


50.25 


52.73 


50.48 


73 


74 


54.12 


50.47 


53.90 


50.70 


53.68 


50.94 


53.45 


51.17 


74 


75 


54.85 


51.15 


54.63 


51.39 


54.40 


51.63 


54.18 


51.86 


75 


76 


55.58 


51.83 


55.36 


52.07 


55.13 


52.31 


54.90 


52.55 


76 

77 ' 


77 


56.31 


52.51 


56.08 


52.76 


55.85 


53.00 


55.62 


53.25 


78 


57.05 


53.20 


56.81 


53.44 


56.58 


53.69 


56.34 


53.94 


78 


79 


57.78 


53.88 


57.54 


54.13 


57.30 


54.38 


57.07 


54.63 


79 


80 


58.51 


54.56 


58.27 


54.81 


58.03 


55.07 


57.79 


55.32 


80 


81 


59.24 


55.24 


59.00 


55.50 


58.76 


55.76 


58.51 


56.01 


81 


82 


59.97 


55.92 


59.73 


56.18 


59.48 


56.45 


59.23 


56.70 


82 


83 


60.70 


56.61 


60.45 


56.87 


60.21 


57.13 


59.96 


57.40 


83 


84 


61.43 


57.29 


61.18 


57.56 


60.93 


57.82 


60.68 


58.09 


34 


85 


62.17 


57.97 


61.91 


58.24 


61.66 


58.51 


61.40 


58.78 


85 


86 


62.90 


58.65 


62.64 


58.93 


62.38 


59.20 


62.12 


59.47 


86 i 


87 


63.63 


59.33 


63.37 


59.61 


63.11 


59.89 


62.85 


60.16 


87 


88 


64.36 


60.02 


64.10 


60.30 


63.83 


60.58 


63.57 


60.85 


88 


89 


65.09 


60.70 


64.82 


60.98 


64.56 


61.26 


64.29 


61.54 


89 ; 


90 


65.82 


61.38 


65.55 


61.67 


65.28 


61.95 i 


65.01 


62.24 


90 


91 


66.55 


62.06 


66.28 


62.35 


66.01 


62.64 


65.74 


62.93 


91 


92 


67.28 


62.74 


67.01 


63.04 


66.73 


63.33 


66.46 


63.62 


92 


93 


68.02 


63.43 


67.74 


63.72 


67.46 


64.02 


67.18 


64.31 


93 


94 


68.75 


64.11 


68.47 


64.41 


68.19 


64.71 


67.90 


65.00 


94 


95 


69.48 


64.79 


69.20 


65.09 


68.91 


65.39 


68.62 


65.69 


95 


96 


70.21 


65.47 


69.92 


65.78 


69.64 


66.08 


69.35 


66.39 


96 


97 


70.94 


66.15 


70.65 


66.46 


70.36 


66.77 


70.07 


67.08 


97 


98 


71.67 


66.84 


71.37 


67.15 


71.09 


67.46 


70.79 


67.77 


98 


1 99 


72.40 


67.52 


72.11 


67.83 


71.81 


68.15 


71.51 


63.46 


99 


100 


73.14 


68.20 


72.84 


68.52 


72.54 


68.84 


72.24 


69.15 


100 


«3 
& 

3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


6 

a 

q 


471 


leg. 


46} Deg. 


46i 


Deg. 


46i Deg. 



3A 



90 



TRAVERSE TABLE 



» 

s 
a 
? 

1 


44 Deg. 


44i Deg. 


44i Deg. 


44} Deg. 


45 Deg. 


c 

V 

s 
o 
? ' 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.72 


0.69 


0.72 


0.70 


0.71 


0.70 


0.71 


0.71 


0.71 


0.71 


2 


1.44 


1.39 


1.43 


1.40 


1.43 


1.40 


1.42 


1.41 


1.41 


1.41 


2 


3 


2.16 


2.08 


2.15 


2-09 


2.14 


2.10 


2.13 


2.11 


2.12 


2.12 


3 


4 


2.88 


2.78 


2.87 


2.79 


2.85 


2.80 


2.84 


2.82 


2.83 


2.83 


4 


5 


3.60 


3.47 


3.58 


3.49 


3.57 


3.50 


3.55 


3.52 


3.54] 3.54 


5 


6 


4.32 


4.17 


4.30 


4.19 


4.28 


4.21 


4.26 


4.22 


4.24 


4.24 


6 


7 


5.04 


4.86 


5.01 


4.88 


4.99 


4.91 


4.97 


4.93 


4.95 


4.95 


7 I 


8 


5.75 


5.56 


5.73 


5.53 


5.71 


5.61 


5.68 


5.63 


5.66 


5.66 


8 





6.47 


6.25 


6.45 


6.28 


6.42 6.31 


6.39 


6.34 


6.36 


6.36 


9 ; 


10 
11 


7.19 


6.95 


7.16 


6.98 


7.13 


7.01 


7.10 


7.04 


7.07 


7.07 


10 | 

11 
is • 


7.91 


7.64 


7.88 


7.68 


7.85 


7.71 


7.81 


7.74 


7.78 


7.78 


12 


8.63 


8.34 


8.60 


8.37 


8.56 


8.41 


8.52 


8.45 


8.49 


8.49 


13 


9.35 


9.03 


9.31 


9.07 


9.27 


9.11 


9.23 


9.15 


9.19 


9.19 


13 ; 


14 


10.07 


9.73 


10.03 


9.77 


9.99 


9.81 


9.94 


9.86 


9.90 


9.90 


14 


15 


10.79 


10.42 


10.74 


10.47 


10.70 


10.51 


10.65 


10.56 


10.61 


10.61 


16 


16 


11.51 


11.11 


11.46 


11.16 


11.41 


11.21 


11.36 


11.26 


11.31 


11.31 


16 


17 


12.23 


11.81 


12.18 


11.86 


12.13 


11.92 


12.07 


11.97 


12.02 12.02 


17 , 


18 


12.95 12.50 


12.89 


12.56 


12.84 


12.62 


12.78 


12.67 


12.7312.73 


18 


19 


13.67 


13.20 


13.61 


13.26 


13.55 


13.32 


13.49 


13.38 


13.43 13.43 


19 


20 


14.39 


13.89 


14.33 


13.96 


14.26 


14.02 


14.20 
14.91 


14.08 
14.78 


14.14 14.14 
14.85 14.85 


20 

„ 


21 


15.11 


14.59 


15.04 


14.65 


14.98 


14.72 


22 


15.83 


15.28 


15.76 


15.35 


1 15.69 


15.42 


15.62 


15.49 


15.56 15.56 


22 


23 


16.54 


15.98 


116.47 


16.05 


1 16.40 


16.12 


16.33 


16.19 


16.26 16.26 


23 


24 


17.26 


16.67 


17.19 


16.75 


17.12 


16.82 


17.04 


16.90 


16.97 16.97 


24 


25 


17.98 


17.37 


17.91 


17.44 


17.83 


17.52 


17.75 
! 18.46 


17.60 


17.68 17.68 


25 


26 


18.70 


18.06 


18.62 


18.14 


18.54 


18.22 


18.30 


18.38jl8.38 


26 


27 


19.42 


18.76 


'19.34 


18-84 


19.26 


18.92 


19.17 


19.01 


19.09J19.09 


27 


28 


20.14 


19.45 


|20.06 


19.54 


19.97 


19.63 


19.89 


19.71 


1 19. 80,19.80 
20.51 20.61 


28 


29 


20.86 


20.15 


120.77 


20.24 


20.68 


20.33 


20.60 


20.42 


SS 


30 


21.58 


20.84 


121.49 


20.93 


21.40 


21.03 


21.31 
22.02 


21.12 
21.82 


21.2121.21 
21. 92121.92 


30 
31 


31 


22.30 


21.53 


22.21 


21.63 


22.11 


21.73 


32 


23.02 


22.23 


22.92 


22.33 


22.82 


22.43 


122.73 


22.53 


22.63[22.63 


32 


33 


23.74 


22.92 


23.64 


23.03 


23.54 


23.13 


123.44 


23.23 


23. £i 23.33 


33; 


34 


24.46 


23.62 


24.35 


23.72 


24.25 


23.83 


124.15 


23.94 


24.04 24.04 


34 I 


35 


25.18 


24.31 


25.07 


24.42 


24.96 


24.53 


24.86 


24.64 


24.75 24.75 




36 


25.90 


25.01 


25.79 


25.12 


25.68 


25.23 


25.57 


25.34 


25.46J25.46 


36 


37 


26.62 


25.70 


26.50 


25.82 


26.39 


25.93 


26.28 


26.05 


26.16j26.16 


5 

39 1 


38 


27.33 


26.40 


27.22 


26.52 


27.10 


26.63 


26.99 


26.75 
27.46 


26.87|26.87 


39 


28.05 


27.09 


27.94 


27.21 


27.82 


27.34 


27.70 


27.58[27.58 


40 


28.77 


27.79 


28.65 


27.91 


28.53 


28.04 


28.41 


28.16 


28.28 28 .2S 

28.99i28.99 


40 

41 


41 


29.49 


28.48 


29.37 


28.61 


29.24 


28.74 


29.12 


28.86 


42 


30.21 


29.18 


30.08 


29.31 


29.96 


29.44 ]! 29.83 


29.57 


29. 70i29.70 


42 


43 


30.93 


29.87 


30.80 


30.00 


30.67 


30. 14,! 30.54 


30.27 


30.41 


30.41 


43 * 


4-1 


31.65 


30.56 


31.52 


30.70 


31.38 


30.84 31.25 


30.98 


31.11 


31.11 


44 


45 


32.37 


31.26 


32.23 


31.40 


32.10 


31 .54 i 31.96 


31.68 


31.82 


31.82 


45 


46 


33.09 


31.95 


32.95 


32.10 


32.81 


32.24 


32.67 


32.38 


32.53 


32.53 


46 


47 


33.81 


32.65 


33.67 


32.80 


33.52 


32.94 


33.38 


33.09 


33.23 33.23 


47 


48 


34.53 


33.34 


34.38 


33.49 


34.24 


33.64 


34.09 


33.79 


33.94 


33.94 


48 


49 


35.25 


34.04 


35.10 


34.19 


34.95 


34.34 


34.80 


34.50 


34.65 


34.65 


49 


50 

• 

a 

Q 


35.97 


34.73 


35.82 


34.89 


35.66 


35.05 
Lat. 


35.51 


35.20 


35.36 


35.36 


50 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Dep. 


Lat. 


Dep. 


Lat. 


o 

c 
rt 

s 


46 Deg. 


45} Deg. 


45i Deg. 


45* Deg. 


45 Deg. 



TRAVERSE TABLE. 



91 



g 

1 

a 
? 


44 Deg. 


44i Deg. 


44i Deg. 


441 Deg. 


45 Deg. 


C 

S3 

o 
? 

51 J 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


51 


36.69 


35.43 


36.53 


35.59 


36.38 


35.75 


36.22 


35.90 


36.06 


36.06 


52 


37.41 


36.12 


37.25 


36.29 


37.09 


36.45 


36.93 


36.61 


36.77 


36.77 


52 11 


53 


38.12 


36.82 


37.96 


36.98 


37.80 


37.15 


37.64 


37.31 


37.48 


37.48 


53 


54 


38.84 


37.51 


38.68 


37.68 


38.52 


37.85 


38.35 


38.02 


38.18 


38.18 


54 


55 


39.56 


38.21 


39.40 


38.38 


39.23 


38.55 


39.06 


38.72 


38.89 


38.89 


55 1 


56 


40.28 


38.90 


40.11 


39.08 


39.94 


39.25 


39.77 


39.42 


39.60 


39.60 


56 \ 


57 


41.00 


39.60 


40.83 


39.77 


40.66 


39.95 


40.48 


40.13 


40.31 


40.31 


57 I 


58 


41.72 


40.29 


41.55 


40.47 


41.37 


40.65 


41.19 


40.83 


41.01 


41.01 


58 J 


59 


42.44 


40.98 


42.26 


41.17 


42.08 


41.35 


41.90 


41.54 


41.72 


41.72 


59 


60 
61 


43.16 


41.68 


42.98 


41.87 


42.79 


42.05 


42.61 


42.24 


42.43 


42.43 
43.13 


60 J 

61 J 


43.88 


42.37 


43.69 


42.57 


43.51 


42.76 


43.32 


42.94 


43.13 


62 


44.60 


43.07 


44.41 


43.26 


44.22 


43.46 


44.03 


43.65 


43.84 


43.84 


62 | 


63 


45.32 


43.76 


45.13 


43.96 


44.93 44.16 


44.74 


44.35 


44.55 


44.55 


63 


64 


46.04 


44.46 


45.84 


44.66 


45.65 44.86 


45.45 


45.06 


45.25 


45.25 


64 


65 


46.76 


45.15 


46.56 


45.36 


46.36 


45.56 


46.16 


45.76 


45.96 


45.96 


65 


66 


47.48 


45.85 


47.28 


46.05 


47.07 


46.26 


46.87 


46.46 


46.67 


46.67 


66 


67 


48.20 


46.54 


47.99 


46.75 


47.79 


46.96 


47.58 


47.17 


47.38 


47.38 


67 


63 


48.92 


47.24 


48.71 


47.45 


48.50 


47.66 


48.29 


47.87 


48.08 


48.08 


68 


69 


49.63 


47.93 


49.42 


48.15 


49.21 


48.36 


49.00 


48.58 


48.79 


48.79 


69 


70 


50.35 


48.63 


50.14 


48.85 


49.93 


49.06 


49.71 


49.28 


49.50 


49.50 
50.20 


70 
71 


71 


51.07 


49.32 


50.86 


49.54 


50.64 


49.76 


50.42 


49.98 


50.20 


72 


51.79 


50.02 


51.57 


50.24 


51.35 


50.47 


51.13 


50.69 


50.91 


50.91 


72 


73 


52.51 


50.71 


52.29 


50.94 


52.07 


51.17 


51.84 


51.39 


51.62 


51.62 


73 


74 


53.23 


51.40 


53.01 


51.64 


52.78 


51.87 


52.55 


52.10 


52.33 


52.33 


74 


75 


53.95 


52.10 


53.72 


52.33 


53.49 


52.57 


53.26 


52.80 


53.03 


53.03 


£ 


76 


54.67 


52.79 


54.44 


53.03 


54.21 


53.27 


53.97 


53.51 


53.74 


53.74 


77 


55.39 


53.49 


55.16 


53.73 


54.92 


53.97 


54.68 


54.21 


54.45 


54.45 


77 | 


78 


56.11 


54.18 


55.87 


54.43 


55.63 


54.67 


55.39 


54.91 


55.15 


55.15 


78 


79 


56.83 


54.88 


56.59 


55.13 


56.35 


55.37 


56.10 


55.62 


55.86 


55.86 


79 


80 
81 


57.55 


55.57 


57.30 


55.82 


57.06 


56.07 


56.81 
57.52 


56.32 


56.57 


56.57 


80 


58.27 


56.27 


58.02 


56.52 


57.77 


56.77 


57.03 


57.28 


57.28 


81 


82 


58.99 


56.96 


58.74 


57.22 


58.49 


57.47 


58.24 


57.73 


57.98 


57.98 


82 


83 


59.71 


57.66 


59.45 


57.92 


59.20 


58.18 


58.95 


58.43 


58.69 


58.69 83 


84 


60.42 


58.35 


60.17 


58.61 


59.91 


58.88 


59.66 


59.14 


59.40 


59.40 


84 


85 


61.14 


59.05 


60.89 


59.31 


60.63 


59.58 


60.37 


59.84 


60.10 


60.10 


85 


86 


61.86 


59.74 


61.60 


60.01 


61.34 


60.28 


61.08 


60.55 


60.81 


60.81 


8? 


87 


62.58 


60.44 


62.32 


60.71 


62.05 


60.98 


61.79 


61.25 


61.52 


61.52 


88 


63.30 


61.13 


63.03 


61.41 


62.77 


61.68 


62.50 


61.95 


62.23 


62.23 


88 


89 


64.02 


61.82 


63.75 


62.10 


63.48 


62.38 


63.21 


62.66 


62.93 


62.93 


89 


90 


64.74 


62.52 


64.47 


62.80 


64.19 


63.08 


63.92 


63.36 


63.64 


63.64 


90 
91 


91 


65.46 


63.21 


65.18 


63.50 


64.91 


63.78 


64.63 


64.07 


64.35 


64.35 


92 


66.18 


63.91 


65.90 


64.20 


65.62 


64.48 


65.34 


64.77 


65.05 


65.05 


92 


93 


66.90 


64.60 


66.62 


64.89 


66.33 


65.18 


66.05 


65.47 


65.76 


65.76 


93 


94 


67.62 


65.30 


67.33 


65.59 


67.05 


65.89 


66.76 


66.18 


66.47 


66.47 


94 


95 


68.34 


65.99 


68.05 


66.29 


67.76 


66.59 


67.47 


66.88 


67.18 


67.18 


95 


96 


69.06 


66.69 


68.76 


66.99 


68.47 


67.29 


68.18 


67.59 


67.88 


67.88 


96 


■ 97 


69.78 


67.38 


69.48 


67.69 


69.19 


67.99 


68.89 


68.29 


68.59 


68.59 


97 


98 


70.50 


68.08 


70.20 


68.38 


69.90 


68.69 


69.60 


68.99 


69.30 


69.30 


98 


99 


71.21 


68.77 


70.91 


69.08 


70.61 


69.39 


70.31 


69.70 


70.00 


70.00 


99 


100 


71.93 


69.47 


71.63 


69.78 


71.33 


70.09 


71.02 


70.40 


70.71 


70.71 


100 

Q 


a 
. .3 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


46 Deg. 


45} Deg. 


45i Deg. 


45* Deg. 


45 Deg. 



A TABLE 

OP 



LOGARITHMS, 



FROM 1 TO 10,000. 



Note. The index of the logarithm of every integer 
number consisting of only one figure is 0, of two figures 
1 , of three figures 2, of four figures 3 ; being always a 
unit less than the number of figures contained in the 
integer number. In this table, as is generally the case, 
the index to the logarithm of every number above 100 is 
omitted ; yet in the operation must be prefixed according 
to this remark; so the logarithm of 700 is 2,84510, and 
of 7000 is 3,84510, and so of the rest. 



No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


1 


0.00000 


21 


1.32222 


41 


1.61278 


61 


1.78533 


81 


1.90849 


2 


0.30103 


22 


1.34242 


42 


1.62325 


62 


1.79239 


82 


1.91381 


3 


0.47712 


23 


1.36173 


43 


1.63347 


63 


1.79934 


83 


1.91908 


4 


0.60206 


24 


1.38021 


44 


1.64345 


64 


1.80618 


84 


1.92423 


5 


0.69897 


25 


1.39794 


45 


1.65321 


65 


1.81291 


85 


1.92942 


6 


0.77815 


26 


1.41497 


46 


1.66276 


66 


1.81954 


86 


1.93450 


7 


0.84510 


27 


1.43136 


47 


1.67210 


67 


1.82607 


87 


1.93952 


8 


0.90309 


28 


1.44716 


48 


1.68124 


68 


1.83251 


88 


1.94443 


9 


0.95424 


29 


1 .46240 


49 


1.69020 


69 


1.83885 


89 


1.94939 


10 


1.00000 


30 


1.47712 


50 


1.69897 


70 


1.84510 


90 


1.95424 


11 


1.04139 


31 


1.49136 


51 


1.70757 


71 


1.85126 


91 


1.95904 


12 


1.07913 


32 


1.50515 


52 


1.71600 


72 


1.85733 


92 


1 96379 


13 


1.11394 


33 


1.51851 


53 


1.72428 


73 


1.86332 


93 


1.96848 


14 


1.14613 


34 


1.53148 


54 


1.73239 


74 


1.86923 


94 


1.97313 


15 


1.17609 


35 


1.54407 


55 


1.74036 


75 


1.87506 


95 


1.97772 


16 


1.20412 


36 


1.55630 


56 


1.74819 


76 


1.88081 


96 


1.98227 


17 


1.23045 


37 


1.56820 


57 


1.75587 


77 


1.88649 


97 


1.98677 


18 


1.25527 


38 


1.57978 


58 


1.76343 


78 


1.89209 


98 


1.99123 


19 


1.27875 


39 


1.59106 


59 


1.77085 


79 


1.89763 


99 


1 . 99564 


20 


1.30103 


40 


1.60206 


60 


1.77815 


80 


1.90309 


100 


2.00000 



Logarithms from 1 to 10,000. 



93 





No. 

loo 





1 


2 


3 

00130 


4 
00173 


5 


6 


7 


8 


9 




00000 


00043 


00087 


00217 


00260 


00303 


00346 


00389 




101 


00432 


00475 


00518 


00561 


00604 


00647 


00689 


00732 


00775 


00817 




10.2 


00860 


00903 


00945 


00988 


01030 


01072 


01115 


01157 


01199 


01242 




103 


01284 


01326 


01368 


01410 


01452 


01494 


01536 


01578 


01620 


01662 




104 


01703 


01745 


01787 


01828 


01870 


01912 


01953 


01995 


02036 


02078 




105 


02119 


02160 


02202 


02243 


02284 


02325 


02366 


02407 


02449 


02490 




106 


02531 


02572 


02612 


02653 


02694 


02735 


02776 


02816 


02857 


02898 




107 


02938 


02979 


03019 


03060 


03100 


03141 


03181 


03222 


03262 


03302 




108 


03342 


03383 


03423 


03463 


03503 


03543 


03583 


03623 


03663 


03703 




109 
110 


03743 
04139 


03782 


03822 
04218 


03862 
04258 


03902 
04297 


03941 


03981 
04376 


04021 
04415 


04060 


04100 
04493 




04179 


04336 


04454 




111 


04532 


04571 


04610 


04650 


04689 


04727 


04766 


04805 


04844 


04883 




112 


04922 


04961 


04999 


05038 


05077 


05115 


05154 


05192 


05231 


05269 




113 


05308 


05346 


05385 


05423 


05461 


05500 


05538 


05576 


05614 


05652 




114 


05690 


05729 


05767 


05805 


05843 


05881 


05918 


05956 


05994 


06032 




115 


06070 


06108 


06145 


06183 


06221 


06258 


06296 


06333 


06371 


06408 




116 


06446 


06483 


06521 


06558 


06595 


06633 


06670 


06707 


06744 


06781 




117 


06819 


06856 


06893 


06930 


06967 


07004 


07041 


07078 


07115 


07151 




118 


07188 


07225 


07262 


07298 


07335 


07372 


07408 


07445 


07482 


07518 




119 
120 


07555 


07591 


07628 


07664 
08027 


07700 
08063 


07737 
08099 


07773 


07809 
08171 


07846 


07882 




07918 


07954 


07990 


08135 


08207 


08243 




121 


08279 


08314 


08350 


08386 


08422 


08458 


08493 


08529 


08565 


08600 




122 


08636 


08672 


08707 


08743 


08778 


08814 


08849 


08884 


08920 


08955 




123 


08991 


09026 


09061 


09096 


09132 


09167 


09202 


09237 


09272 


09307 




124 


09342 


09377 


09412 


09447 


09482 


09517 


09552 


09587 


09621 


09656 




125 


09691 


09726 


09760 


09795 


09830 


09864 


09899 


09934 


09968 


10003 




126 


10037 


10072 


10106 


10140 


10175 


10209 


10243 


10278 


10312 


10346 




127 


10380 


10415 


10449 


10483 


10517 


10551 


10585 


10619 


10653 


10687 




128 


10721 


10755 


10789 


10823 


10857 


10890 


10924 


10958 


10992 


11025 




129 
130 


11059 


11093 


11126 


11160 
11494 


11193 


11227 
11561 


11261 


11294 


11327 
11661 


11361 
11694 




11394 


11428 


11461 


11528 


11594 


11628 




131 


11727 


11760 


11793 


11826 


11860 


11893 


11926 


11959 


11992 


12024 




132 


12057 


12090 


12123 


12156 


12189 


12222 


12254 


12287 


12320 


12352 




133 


12385 


12418 


12450 


12483 


12516 


12548 


12581 


12613 


12646 


12678 




134 


12710 


12743 


12775 


12808 


12840 


12872 


12905 


12937 


12969 


13001 




135 


13033 


13066 


13098 


13130 


13162 


13194 


13226 


13258 


13290 


13322 




136 


13354 


13386 


13418 


13450 


13481 


13513 


13545 


13577 


13609 


13640 




137 


13672 


13704 


13735 


13767 


13799 


13830 


13862 


13893 


13925 


13956 




138 


13988 


14019 


14051 


14082 


14114 


14145 


14176 


14208 


14239 


14270 




139 


14301 


14333 


14364 


14395 


14426 


14457 


14489 


14520 


| 14551 


14582 




140 


14613 


14644 


14675 


14706 


14737 


14768 


14799 


14829 


14860 


14891 




141 


14922 


14953 


14983 


15014 


15045 


15076 


15106 


15137 


15168 


15198 




142 


15229 


15259 


15290 


15320 


15351 


15381 


15412 


15442 


15473 


15503 




143 


15534 


15564 


15594 


15625 


15655 


15685 


15715 


15746 


15776 


15806 




144 


15836 


15866 


15897 


15927 


15957 


15987 


16017 


16047 


16077 


16107 




145 


16137 


16167 


16197 


16227 


16256 


16286 


16316 


16346 


16376 


16406 




146 


16435 


16465 


16495 


16524 


16554 


16584 


16613 


16643 


16673 


16702 




147 


16732 


16761 


16791 


16820 


16850 


16879 


16909 


16938 


16967 


16997 i 




148 


17026 


17056 


17085 


17114 


17143 


17173 


17202 


17231 


17260 


17289 




149 
150 


17319 
17609 


17348 
17638 


17377 


17406 


17435 

17725 


17464 


17493 


17522 
17811 


17551 
17840 


17580 
17869 




17667 


17696 


17754 


17782 




151 


17898 


17926 


17955 


17984 


18013 


18041 


18070 


18099 


18127 


18156 




152 


18184 


18213 


18241 


18270 


18298 


18327 


18355 


18384 


18412 


18441 




153 


18469 


18498 


18526 


18554 


18583 


18611 


18639 


18667 


18696 


18724 




154 


18752 


18780 


18808 


18837 


18865 


18893 


18921 


18949 


18977 


19005 




155 


19033 


19061 


19089 


19117 


19145 


19173 


19201 


19229 


19257 


19285 




156 


19312 


19340 


19368 


19396 


19424 


19451 


19479 


19507 


19535 


19562 




I 1/57 


19590 


19618 


19645 


19673 


19700 


19728 


19756 


19783 


19811 


19838 




158 


19866 


19893 


19921 


19948 


19976 


20003 


20030 


20058 


20085 


20112 




159 


1 20140 


20167 


20194 


20222 


20249 


20276 


20303 


20330 


20358 


20385 



32 



01 



Logarithms from 1 to 10,000. 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


1 9 




160 


20412 


20439 


20466 


20493 


20520 


20548 


20575 


20602 


20629 


! 20656 




161 


20683 


20710 


20737 


20763 


20790 


20817 


20844 


201.71 


20898 


20925 




162 


20952 


20978 


21005 


21032 


21059 


21085 


21112 


21139 


21165 


21192 




! 168 


21219 


21245 


21272 


21299 


21325 


21352 


21878 


21405 


21431 


21458 




164 


21484 


21511 


21537 


21564 


21590 


21617 


21643 


21669 


21696 


21722 




.! 165 


21748 


21775 


21801 


21827 


21854 


21880 


21906 


21982 


21958 


219;.:, 




i 166 


22011 


22037 


22063 


22089 


22115 


22 141 


22167 


22194 


22220 






167 


22272 


22298 


22324 


22350 


22376 


22401 


22427 


22453 


22479 


22605 




168 


22531 


22557 


22583 


22608 


22634 


22660 


22686 


227 1 2 


22737 


22763 




169 

no 


22789 
23045 


22814 
23070 


22840 


22866 
23121 


22891 
23147 


22917 


22943 
23198 


22968 

28223 


22994 
23249 


28019 

28-74 




23096 


23172 




171 


23300 


23325 


23350 


23376 


23401 


23426 


28452 


28477 


23502 






172 


23553 


23578 


23603 


23629 


23654 


23679 


23704 


23729 


2375 1 






173 


23805 


23830 


23855 


23880 


23905 


23930 


23955 


23980 


24005 


24030 




174 


24055 


24080 


24105 


24130 


24155 


24180 


24204 


24229 


24254 


24279 




175 


24304 


24329 


24353 


24378 


24403 


24428 


21452 


24477 


24502 


24527 




176 


24551 


24576 


24601 


24625 


24650 


24674 


24699 


24724 


24748 


24773 




177 


24797 


24822 


24846 


24871 


24895 


24920 


24944 


24969 


24993 


25018 




178 


25042 


25066 


25091 


25115 


25139 


25164 


25188 


25212 


25237 


25261 




179 
ISO 


25285 


25310 
25551 


25334 
25575 


25358 

25600 


25382 
25624 


25406 


25431 
25672 


25455 
25696 


25479 
25720 


25503 
25744 




25527 


25648 




181 


25768 


25792 


25816 


25840 


25864 


25888 


25912 


25935 


25959 


25983 




182 


26007 


26031 


26055 


26079 


26102 


26126 


26150 


26174 


26198 


26221 




183 


26245 


26269 


26293 


26316 


26340 


26364 


26387 


26411 


26435 


26458 




184 


26482 


26505 


26529 


26553 


26576 


26600 


26623 


26647 


26670 


26694 




185 


26717 


26741 


26764 


26788 


26811 


26834 


26858 


26881 


26905 


26928 




186 


26951 


26975 


26998 


27021 


27045 


27068 


27091 


27114 


27138 


27161 




187 


27184 


27207 


27231 


27254 


27277 


27300 


27323 


27346 


27370 


27393 




188 


27416 


27439 


27462 


27485 


27508 


27531 


27554 


27577 


27600 


27623 




189 
190 


27646 


27669 


27692 


27715 


27738 
27967 


27761 
27989 


27784 


27807 


27830 


27852 

28081 




27875 


27898 


27921 


27944 


28012 


23035 


28058 




191 


28103 


28126 


28149 


28171 


28194 


28217 


28240 


28262 


28285 


28307 




192 


28330 


28353 


28375 


28398 


28421 


28443 


28466 


28488 


28511 


28533 




193 


28556 


28578 


28601 


28623 


28646 


28668 


28691 


28713 


28735 


28758 




194 


28780 


28803 


28325 


28847 


28870 


28892 


28914 


28937 


28959 


28981 




195 


29003 


29026 


29048 


29070 


29092 


29115 


29137 


29159 


29181 


29203 




196 


29226 


29248 


29270 


29292 


29314 


29336 


29353 


29380 


29403 


29425 




197 


29447 


29469 


29491 


29513 


29535 


29557 


29579 


29601 


29623 


29645 




198 


29667 


29688 


29710 


29732 


29754 


29776 


29798 


29820 


29842 


29863 




199 
200 


29885 
30103 


29907 
30125 


29929 
30146 


29951 


29973 
30190 


29994 
30211 


30016 
30233 


30038 
80255 


30060 
30276 


30081 
30298 




30168 




1201 


30320 


30341 


30363 


30384 


30406 


30428 


30449 


80471 


30492 


30514 




,202 


30535 


30557 


30578 


30600 


30621 


30643 


30664 


30685 


30707 


30728 




203 


30750 


30771 


30792 


30814 


30835 


30856 


30878 


30899 


30920 


30942 




204 


30963 


30984 


31006 


31027 


31048 


31069 


31091 


31112 


31133 


31154 




205 


31175 


31197 


31218 


31239 


31260 


31281 


31802 


31323 


31515 


31366 




206 


31387 


31408 


31429 


31450 


31471 


31492 


31513 


31534 


31555 


31576 




207 


31597 


31618 


31639 


31660 


31681 


31702 


31723 


31744 


31765 


31785 




208 


31806 


31827 


31848 


31869 


31890 


31911 


31931 


81952 


31973 


31994 




209 
210 


32015 


32035 
32243 


32056 


32077 


32093 
32305 


32118 
32325 


32139 
32346 


32160 
32366 


32181 
32387 


32201 
32408 




32222 


32263 


32284 




211 


32428 


32449 


32469 


32490 


32510 


32531 


32552 


32572 


32593 


32613 




212 


32634 


32654 


32675 


32695 


32715 


32736 


32756 


32777 


32797 


32818 




213 


32838 


32858 


32879 


32899 


32919 


32940 


32960 


32980 


33001 


33021 




214 


33041 


33062 


33082 


33102 


33122 


33143 


33163 


33183 


33203 


33224 




215 


33244 


33264 


33284 


33304 


33325 


33345 


33365 


33885 


33405 


33425 




216 


33445 


33465 


33486 


33506 


33526 


33546 


33566 


33586 


33606 


33626 




217 


33646 


33666 


33686 


33706 


33726 


33746 


33766 


33786 


33806 


33826 




218 


33846 


33866 


33885 


33905 


33925 


33945 


33965 


33985 


34005 


34025 




219| 


34044 


34064 


34084 


34104 1 


34124 


34143 


34163 


34183 1 


34203 


34223 





Logarithms from 1 to 10,000. 



95 



' iNo. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


220 


34242 


34262 


34282 


34301 


34321 


34341 


34361 


34380 


34400 


3442Q 


221 


34439 


34459 


34479 


34498 


34518 


34537 


34557 


34577 


34596 


34616 


222 


34635 


34655 


34674 


34694 


34713 


34733 


34753 


34772 


34792 


34811 


223 


34830 


34850 


34869 


34889 


34908 


34928 


34947 


34967 


34986 


35005 


224 


35025 


35044 


35064 


35083 


35102 


35122 


35141 


35160 


35180 


35199 


225 


35218 


35238 


35257 


35276 


35295 


35315 


35334 


35353 


35372 


35392 


226 


35411 


35430 


35449 


35468 


35488 


35507 


35526 


35545 


35564 


35583 


227 


35603 


35622 


35641 


35660 


35679 


35698 


35717 


35736 


35755 


35774 


228 


35793 


35813 


35832 


35851 


35870 


35889 


35908 


35927 


35946 


35965 


229 


359S4 


36003 


36021 


36040 


36059 


36078 


36097 


36116 


36135 


36154 


230 


36173 


36192 


36211 


36229 


36248 


36267 


36286 


36305 


36324 


36342 . 


231 


36361 


36380 


36399 


36418 


36436 


36455 


36474 


36493 


36511 


26530 


232 


36549 


36568 


36586 


36605 


36C24 


36642 


36661 


36680 


36698 


36717 


233 


36736 


36754 


36773 


36791 


36810 


36829 


36847 


36866 


36884 


36903 


234 


36922 


36940 


36959 


36977 


36996 


37014 


37033 


37051 


37070 


37088 


235 


37107 


37125 


37144 


37162 


37181 


37199 


37218 


37236 


37254 


37273 


236 


37291 


37310 


37328 


37346 


37365 


37383 


37401 


37420 


37438 


37457 


237 


37475 


37493 


37511 


37530 


37548 


37566 


37585 


37603 


37621 


37639 


238 


37658 


37676 


37694 


37712 


37731 


37749 


37767 


37785 


37803 


37822 


239 
240 


37840 
38021 


37858 
38039 


37876 
38057 


37894 
38075 


37912 
38093 


37931 
38112 


37949 
38130 


37967 
38148 


37985 
38166 


38003 


38184 


241 


38202 


38220 


38238 


38256 


38274 


38292 


38310 


38328 


38346 


38364 


242 


38382 


38399 


38417 


38435 


38453 


38471 


38489 


38507 


38525 


38543 


243 


38561 


38578 


38596 


38614 


38632 


38650 


38668 


38686 


38703 


38721 


244 


38739 


38757 


38775 


38792 


38810 


38828 


38846 


38863 


38881 


38899 


245 


38917 


38934 


38952 


38970 


38987 


39005 


39023 


39041 


39058 


39076 


246 


39094 


39111 


39129 


39146 


39164 


39182 


39199 


39217 


39235 


39252 


247 


39270 


39287 


39305 


39322 


39340 


39358 


39375 


39393 


39410 


39428 


248 


39445 


39463 


39480 


39498 


39515 


39533 


39550 


39568 


39585 


39602 


249 
250 


39620 
39794 


39637 
39811 


39655 
39829 


39672 
39846 


39690 


39707 
39881 


39724 
39898 


39742 
39915 


39759 
39933 


39777 
39950 


39863 


251 


39967 


39985 


40002 


40019 


40037 


40054 


40071 


40088 


40106 


40123 


252 


40140 


40157 


40175 


40192 


40209 


40226 


40243 


40261 


40278 


40295 


253 


40312 


40329 


40346 


40364 


40381 


40398 


40415 


40432 


40449 


40466 


254 


40483 


40500 


40518 


40535 


40552 


40569 


40586 


40603 


40620 


40637 


255 


40654 


40671 


40688 


40705 


40722 


40739 


40756 


40773 


40790 


40807 


256 


40824 


40841 


40858 


40875 


40892 


40909 


40926 


40943 


40960 


40976 


257 


40993 


41010 


41027 


41044 


41061 


41078 


41095 


41111 


41128 


41145 


258 


41162 


41179 


41196 


41212 


41229 


41246 


41263 


41280 


41296 


41313 


259 
' 260 


41330 
41497 


41347 
41514 


41363 


41380 
41547 


41397 
41564 


41414 
41581 


41430 
41597 


41447 
41614 


41464 
41631 


41481 
41647 


41531 


261 


41664 


41681 


41697 


41714 


41731 


41747 


41764 


41780 


41797 


41814 


262 


41830 


41847 


41863 


41880 


41896 


41913 


41929 


41946 


41963 


41979 


263 


41996 


42012 


42029 


42045 


42062 


4207b ) 42095 


42111 


42127 


42144 


264 


42160 


42177 


42193 


42210 


42226 


42243 


42259 


42275 


42292 


42308 


265 


42325 


42341 


42357 


42374 


42390 


42406 


42423 


42439 


42455 


42472 


266 


42488 


42504 


42521 


42537 


42553 


42570 


42586 


42602 


42619 


42635 


267 


42651 


42667 


42684 


42700 


42716 


42732 


42749 


42765 


42781 


42797 


268 


42813 


42830 


42846 


42862 


42878 


42894 


42911 


42927 


42943 


42959 


269 


42975 


42991 


43008 


43024 


43040 


43056 


43072 


43088 


43104 


13120 


270 


43136 


43152 


43169 


43185 


43201 


43217 


43233 


43249 


43265 


43281 


271 


43297 


43313 


43329 


43345 


43361 


43377 


43393 


43409 


43425 


43441 


272 


43457 


43473 


43489 


43505 


43521 


43537 


43553 


43569 


43584 


43600 


273 


43616 


43632 


43648 


43664 


43680 


43696 


43712 


43727 


43743 


43759 


274 


43775 


43791 


43807 


43823 


43838 


43854 


43870 


43886 


43902 


43917 


;275 


43933 


43949 


43965 


43981 


43996 


44012 


44028 


44044 


44059 


44075 


276 


44091 


44107 


44122 


44138 


44154 


44170 


44185 


44201 


44217 


44232 


'277 


44248 


44264 


44279 


44295 


44311 


44326 


44342 


44358 


44373 


44389 


278 


44404 


44420 


44436 


44451 


44467 


44483 


44498 


44514 


44529 


44545 


279 


44560 


44576 


44592 


44607 


44623 


44638 


44654 


44669 


44685 | 


44700 



96 



Logarithms from 1 to 10,000. 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 




280 


44716 


44731 


44747 


44762 


44778 


44793 


44809 


44824 


44840 


44855 




281 


44871 


44886 


44902 


44917 


44932 


44943 


44963 


44979 


44994 


45010 




282 


45025 


45040 


45056 


45071 


45086 


45102 


45117 


45133 


45148 


45163 




283 


45179 


45194 


45209 


45225 


45240 


45255 


45271 


45286 


45301 


45317 




2fl4 


45332 


45347 


45362 


45378 


45393 


45408 


45423 


45439 


45454 


45469 




285 


45484 


45500 


45515 


45530 


45545 


45561 


45576 


45591 


45606 


45621 




286 


45637 


45652 


45667 


45682 


45697 


45712 


45728 


45743 


45758 


45773 




287 


45788 


45803 


45818 


45834 


45849 


45864 


45879 


45894 


45909 


45924 




288 


45939 


45954 


45969 


45984 


46000 


46015 


46030 


46045 


46060 


46075 




289 


46090 


46105 


46120 


46135 


46150 


46165 


46180 


46195 


46210 


46225 




290 


46240 


46255 


46270 


46285 


46300 


46315 


46330 


46345 


46359 


4637 . 




291 


46389 


46404 


46419 


46434 


46449 


46464 


46479 


46494 


46509 


46523 




292 


46538 


46553 


46568 


46583 


46598 


46613 


46627 


46642 


4o657 


46672 




293 


46687 


46702 


46716 


46731 


46746 


46761 


46776 


46790 


46805 


46820 




294 


46835 


46850 


46864 


46879 


46894 


46909 


46923 


46938 


46953 


46967 




■ 295 


46982 


46997 


47012 


47026 


47041 


47056 


47070 


47085 


47100 


47114 




296 


47129 


47144 


47159 


47173 


47188 


47202 


47217 


47232 


47246 


47261 




297 


47276 


47290 


47305 


47319 


47334 


47349 


47363 


47378 


47392 


47407 




298 


47422 


47436 


47451 


47465 


47480 


47494 


47509 


47524 


47538 


47553 




299 
300 


47567 

47712 


47582 

47727 


47596 
47741 


47611 
47756 


47625 
47770 


47640 
47784 


47654 


47669 
47813 


47683 
47828 


47698 
47842 




47799 




'301 


47857 


47871 


47885 


47900 


47914 


47929 


47943 


47958 


47972 


47986 




302 


48001 


48015 


48029 


48044 


48058 


48073 


48087 


48101 


48116 


48130 




i 303 


48144 


48159 


43173 


48187 


48202 


48216 


48230 


48244 


48259 


48273 




! 304 


48287 


48302 


48316 


48330 


48344 


48359 


48373 


48387 


48401 


48416 




305 


48430 


48444 


48458 


48473 


48487 


48501 


48515 


48530 


48544 


48558 




306 


48572 


48586 


48601 


48615 


48629 


48643 


48657 


48671 


48686 


48700 




»307 


48714 


48728 


48742 


48756 


48770 


48785 


48799 


48813 


48827 


48841 




308 


48855 


43369 


48883 


48897 


48911 


48926 


48940 


48954 


48968 


48982 




309 


48996 


49010 


49024 


49038 


49052 


49066 


49080 


49094 


49108 


49122 




310 


49136 


49150 


49164 


49178 


49192 


49206 


49220 


49234 


49248 


49262 




311 


49276 


49290 


49304 


49318 


49332 


49346 


49360 


49374 


49388 


49402 




312 


49415 


49429 


49443 


49457 


49471 


49485 


49499 


49513 


49527 


49541 




313 


49554 


49568 


49582 


49596 


49610 


49624 


49638 


49651 


49665 


49679 




'314 


49693 


49707 


49721 


49734 


49748 


49762 


49776 


49790 


49803 


49817 




315 


49831 


49845 


49859 


49872 


49886 


49900 


49914 


49927 


49941 


49955 




•316 


49969 


49982 


49996 


50010 


50024 


50037 


50051 


50065 


50079 


50092 




317 


50106 


50120 


50133 


50147 


50161 


50174 


50188 


50202 


50215 


50229 




318 


50243 


50256 


50270 


50284 


50297 


50311 


50325 


50333 


50352 


50365 




319 


50379 


50393 


50406 


50420 


50433 


50447 


50461 


50474 


50488 


50501 




320 


50515 


50529 


50542 


50556 


50569 


50583 


50596 


50610 


50623 


50637 




321 


50651 


50664 


50678 


50691 


50705 


50718 


50732 


50745 


50759 


50772 




322 


50786 


50799 


50813 


50826 


50840 


50853 


50866 


50880 


50893 


50907 




323 


50920 


50934 


50947 


50Q6 1 


50974 


50987 


51001 


51014 


51028, 51041 




324 


51055 


51068 


51081 


51095 


51108 


51121 


51135 


51148 


51162.51175 




325 


51188 


51202 


51215 


51228 


51242 


51255 


51268 


51282 


51295 51308 




326 


51322 


51335 


51348 


51362 


51375 


51388 


51402 


51415 


51428 


51441 




327 


51455 


51468 


51481 


51495 


51508 


51521 


51534 


51543 


51561 


51574 




328 


51587 


51601 


51614 


51627 


51640 


51654 


51667 


51680 


51693 


51706 




329 
330 


51720 
51851 


51733 
51865 


51746 
51878 


51759 
51891 


51772 
51904 


51786 
51917 


51799 


51812 


51825 
51957 


51838 
H970 




51930 


51943 




331 


51983 


51996 


52009 


53022 


52035 


52048 


52061 


52075 


52088 


52101 




332 


52114 


52127 


52140 


52153 


52166 


52179 


52192 


52205 


52218 


52231 




333 


52244 


52257 


52270 


52284 


52297 


52310 


52323 


52336 


52349 


52362 




334 


52375 


52388 


52401 


52414 


52427 


52440 


52453 


52466 


52479 


52492 




335 


52504 


52517 


52530 


52543 


52556 


52569 


52582 


52595 


52608 


52621 




336 


52634 


52647 


52660 


52673 


52686 


52699 


52711 


52724 


52737 


52750 




337 


52763 


52776 


52789 


52802 


52815 


52827 


52840 


52853 


52866 


52879 




338 


52892 


52905 


52917 


52930 


52943 


52956 


52969 


52982 


52994 


53007 1 


339 53020 


53033 


53046 


53058 


53071 


53084 


53097 


53110 1 


53122 


53135 1 





Logarithms from 1 to 10,000. 



97 



No. 

340 
341 
342 
343 
344 
345 
346 

1347 

'348 
349 
350 
351 
352 
353 
354 
355 
356 
357 
358 
359 
360 
361 
362 
363 
364 
365 
366 

.367 
368 
369 
370 
371 

•372 
373 
374 
375 
376 
377 
378 
379 
380 
381 
382 

. 383 
384 
385 
386 
387 
388 
389 
390 
391 
392 
393 

■ 394 
395 

'396 
397 
398 

^399 





1 


2 


3 


4 

53199 
53326 
53453 
53580 
53706 
53832 
53958 
54083 
54208 
54332 
54456 
54580 
54704 
54827 
54949 
55072 
55194 
55315 
55437 
55558 
55678 
55799 
55919 
56038 
56158 
56277 
56396 
56514 
56632 
56750 
56867 
56984 
57101 
57217 
57334 
57449 
57565 
57680 
57795 
57910 
58024 
58138 
58252 
58365 
58478 
58591 
58704 
58816 
58928 
59040 
59151 
59262 
59373 
59483 
59594 
59704 
59813 
59923 
60032 
60141 


5 


6 


7 


8 

53250 
53377 
53504 
53631 
53757 
53882 
54008 
54133 
54258 
54382 
54506 
54630 
54753 
54876 
54998 
55151 
55242 
55364 
55485 
55606 
55727 
55847 
55967 
56086 
56205 
56324 
56443 
56561 
56679 
56797 
56914 
57031 
57148 
57264 
57380 
57496 
57611 
57726 
57841 
57955 
58070 
58184 
58297 
58410 
58524 
58636 
58749 
58861 
58973 
59084 
59195 
59306 
59417 
59528 
59638 
59748 
59857 
59966 
60076 
60184 


9 


53148 
53275 
53403 
53529 
53656 
53782 
53908 
54033 
54158 
54283 
54407 
54531 
54654 
54777 
54900 
55023 
55145 
55267 
55388 
55509 
55630 
55751 
55871 
55991 
56110 
56229 
56348 
56467 
56585 
56703 
56820 
56937 
57054 
57171 
57287 
57403 
57519 
57634 
57749 
57864 
57978 
58092 
58206 
58320 
58433 
58546 
58659 
58771 
58883 
58995 
59106 
59218 
59329 
59439 
59550 
5966U 
59770 
59879 
59988 
60097 


531S1 
53288 
53415 
53542 
5366-° 
53794 
53920 
54045 
54170 
54295 
54419 
54543 
54667 
54790 
54913 
55035 
55157 
55279 
55400 
55522 
55642 
55763 
55883 
56003 
56122 
56241 
56360 
56478 
56597 
56714 
56832 
56949 
57066 
57183 
57299 
57415 
57530 
57646 
57761 
57875 
57990 
58104 
58218 
58331 
58444 
58557 
58670 
58782 
58894 
59006 
59118 
59229 
59340 
59450 
59561 
59671 
59780 
59890 
59999 
60108 


53173 
53301 
53428 
53555 
53681 
53807 
53933 
54058 
54183 
54307 
54432 
54555 
54679 
54802 
54925 
55047 
55169 
55291 
55413 
55534 
55654 
55775 
55895 
56015 
56134 
56253 
56372 
56490 
56608 
56726 
56844 
56961 
57078 
57194 
57310 
57426 
57542 
57657 
57772 
57887 
58001 
58115 
58229 
58343 
58456 
58569 
58681 
58794 
58906 
59017 
59129 
59240 
59351 
59461 
59572 
59682 
59791 
59901 
60010 
60119 


53186 
53314 
53441 
53567 
53694 
53820 
53945 
54070 
54195 
54320 
54444 
54568 
54691 
54814 
54937 
55060 
55182 
55303 
55425 
55546 
55666 
55787 
55907 
56027 
56146 
56265 
56384 
56502 
56620 
56738 
56855 
56972 
57089 
57206 
57322 
57438 
57553 
57669 
57784 
57898 
58013 
58127 
58240 
58354 
58467 
58580 
58692 
58805 
58917 
59028 
59140 
59251 
59362 
59472 
59583 
59693 
59802 
59912 
60021 
60130 


53212 
53339 
53466 
53593 
53719 
53845 
53970 
54095 
54220 
54345 
54469 
54593 
54716 
54839 
54962 
55084 
55206 
55328 
55449 
55570 
55691 
55811 
55931 
56050 
56170 
56289 
56407 
56526 
56644 
56761 
56879 
56996 
57113 
57229 
57345 
57461 
57576 
57692 
57807 
57921 
58035 
58149 
58263 
58377 
58490 
58602 
58715 
58827 
58939 
59051 
59162 
59273 
59384 
59494 
59605 
59715 
59824 
59934 
60043 
60152 


53224 
53352 
53479 
53605 
53732 
53857 
53983 
54108 
54233 
54357 
54481 
54605 
54728 
54851 
54974 
55096 
55218 
55340 
o5461 
55582 
55703 
55823 
55943 
56062 
56182 
56301 
56419 
56538 
56656 
56773 
56891 
57008 
57124 
57241 
57357 
57473 
57588 
57703 
57818 
57933 
58047 
58161 
58274 
58388 
58501 
58614 
58726 
58838 
58950 
59062 
59173 
59284 
59395 
59506 
59616 
59726 
59835 
59945 
60054 
60163 


53237 
53364 
53491 
53618 
53744 
53870 
53995 
54120 
54245 
54370 
54494 
54617 
54741 
54864 
54986 
55108 
55230 
55352 
55473 
55594 
55715 
55835 
55955 
56074 
56194 
56312 
56431 
56549 
56667 
56785 
56902 
57019 
57136 
57252 
57368 
57484 
57600 
57715 
57830 
57944 
58058 
58172 
58286 
58399 
58512 
58625 
58737 
58850 
58961 
59073 
59184 
59295 
59406 
59517 
59627 
59737 
59846 
59956 
60065 
60173 


53263 
53390 
53517 
53643 
53769 
53895 
54020 
54145 
54270 
54394 
54518 
54642 
54765 
54888 
55011 
55133 
55255 
55376 
55497 
55618 


55739 
55859 
55979 
56098 
56217 
56336 
56455 
56573 
56691 
56808 
56926 
57043 
57159 
57276 
57392 
57507 
57623 
57738 
57852 
57967 
58081 
58195 
58309 
58422 
58535 
58647 
58760 
58872 
58984 
59095 
59207 
59318 
59428 
59539 
59649 
59759 
59868 
59977 
60086 
60195 



23* 



3B 



G8 



Logarithms from 1 to 10,000. 



No. 

400 





1 


2 


3 


4 


5 


6 


7 


8 


9 


60206 


60217 


60228 


60239 


60249 


60260 


6027 1 


60282 


60293 


60304 


401 


60314 


60325 


60336 


60347 


60358 


60369 


60379 


60390 


60401 


60412 


402 


60423 


60433 


60444 


60455 


60466 


60477 


60487 


60198 


60509 


60520 


403 


60531 


60541 


60552 


60563 


60574 


60584 


60595 


60606 


60617 


60627 


404 


60638 


60649 


60660 


60670 


60681 


60692 


60703 


60713 


60724 


60735 


405 


60746 


60756 


60767 


60778 


60788 


60799 


60810 


60821 


60831 


60842 


406 


60853 


60863 


60874 


60885 


60895 


60906 


60917 


60921 


60938 


60949 


407 


60959 


60970 


60981 


60991 


61002 


61013 


61023 


61034 


61045 


61055 


408 


61066 


61077 


61087 


61098 


61109 


61119 


61130 


61140 


61151 


61162 


409 


61172 


61183 


61194 


61204 


61215 


61225 


61236 


61247 


61257 


61268 


410 


61278 


61289 


61300 


61310 


61321 


61331 


61342 


61352 


61363 


61374 


411 


61384 


61395 


61405 


61416 


61426 


61437 


61448 


61458 


61469 


61479 


412 


61490 


61500 


61511 


61521 


61532 


61542 


61553 


6 1 5V>:1 


61574 


61584 


413 


61595 


61606 


61616 


61627 


61637 


61648 


61653 


61669 


61679 


61690 


414 


61700 


61711 


61721 


61731 


61742 


61752 


61763 


61773 


61784 


61794 


415 


61805 


61815 


61826 


61836 


61847 


61857 


61868 


61878 


61888 


61899 


416 


61909 


61920 


61930 


61941 


61951 


61962 


61972 


61982 


61993 


6 .'(Hi;; 


417 


62014 


62024 


62034 


62045 


62055 


62066 


62076 


62086 


62097 


62107 


418 


62118 


62128 


62138 


62149 


62159 


62170 


62180 


62190 


62201 


6221! 


419 


62221 


62232 


62242 


62252 


62263 


62273 


62284 


62294 


62304 


62315 


420 


62325 


62335 


62346 


62356 


62366 


62377 


62387 


62397 


62408 


62418 


421 


62428 


62439 


62449 


62459 


62469 


62480 


62490 


62500 


62511 


6252 1 


422 


62531 


62542 


62552 


62562 


62572 


62583 


62593 


62603 


62613 


62024 


423 


62634 


62644 


62655 


62665 


62675 


62685 


62696 


62706 


62716 


62726 


424 


62737 


62747 


62757 


62767 


62778 


62788 


62798 


62808 


62818 


62829 


425 


62839 


62849 


62859 


62870 


62880 


62890 


62900 


62910 


62921 


62931 


426 


62941 


62951 


62961 


62972 


62982 


62992 


63002 


63012 


63022 


63033 


427 


63043 


63053 


63063 


63073 


63083 


63094 


63104 


63114 


63124 


63134 


428 


63144 


63155 


63165 


63175 


63185 


63195 


63205 


63215 


63225 


63236 


429 


63246 


63256 


63266 


63276 


63286 


63296 


63306 


63317 


63327 


63337 


430 


63347 


63357 


63367 


63377 


63387 


63397 


63407 


63417 


63428 


63438 


431 


63448 


63458 


63468 


63478 


63488 


63498 


63508 


63518 


63528 


63538 


432 


63548 


63558 


63563 


63579 


63589 


63599 


63609 


63619 


63629 


63639 


433 


63649 


63659 


63669 


63679 


63689 


63699 


63709 


63719 


63729 


63739 


434 


63749 


63759 


63769 


63779 


63789 


63799 


63809 


63819 


63829 


63839 


435 


63849 


63859 


63869 


63879 


63889 


63899 


63909 


63919 


63929 


63939 


436 


63949 


63959 


63969 


63979 


63988 


63998 


64008 


64018 


64028 


64038 


437 


64048 


64058 


64063 


64078 


64083 


64098 


64108 


64118 


64128 


64137 


438 


64147 


64157 


64167 


64177 


64187 


64197 


64207 


64217 


64227 


64237 


439 
440 


64246 
64345 


64256 
64355 


64266 
64365 


64276 
64375 


64286 
64385 


64296 
64395 


64306 
64404 


64316 
64414 


64326 

64424 


64335 


64434 


441 


64444 


64454 


64464 


64473 


64483 


64493 


64503 


64513 


64523 


61532 


442 


64542 


64552 


64562 


64572 


64582 


64591 


64601 


64611 


64621 


64631 


443 


64640 


64650 


64660 


64670 


64680 


64689 


64699 


64709 


64719 


64729 


444 


64738 


64748 


64758 


64768 


64777 


64787 


64797 


64807 


64816 


64826 


445 


64336 


64846 


64856 


64865 


64875 


64885 


64895 


64904 


64914 ' 64921 


446 


64933 


64943 


64953 


64963 


64972 


64982 


64992 


65002 


65011 i 65021 


447 


65031 


65040 


65050 


65060 


65070 


65079 


65089 


65099 


65108! 55118 


448 


65128 


65137 


65147 


65157 


65167 


65176 


05186 


65196 


65205 S5215 


449 
450 


65225 


65234 


65244 
65341 


65254 
65350 


65263 
65360 


65273 
65369 


65283 
65379 


65292 


65302 55312 


65321 


65331 


65389 


65398 


O5408 


451 


65418 


65427 


65437 


65447 


65456 


65466 


65475 


65485 


65195 


65504 


452 


65514 


65523 


65533 


65543 


65552 


65562 


65571 


65581 


65591 


65600 


453 


65610 


65619 


65629 


65639 


65648 


65658 


65667 


65677 


65686 


65696 


454 


65706 


65715 


65725 


65734 


65744 


65753 


65763 


65772 


65782 


65792 


455 


65801 


65811 


65820 


65830 


65839 


65849 


65858 


65868 


65877 


65887 


456 


65896 


65906 


65916 


65925 


65935 


65944 


65954 


65963 


65973 


65982 


•457 


65992 


66001 


66011 


66020 


66030 


66039 


66049 


66058 


66068 


66077 


458 


66087 


66096 


66106 


66115 


66124 


66134 


66143 


66153 


66162 


66172 


459 


66181 


66191 


66200 


66210 


66219 


66229 


66238 


66247 


66257 


66266 



Logarithms from 1 to 10,000. 



99 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 




460 


66276 


66285 


66295 


66304 


66314 


66323 


66332 


66342 


66351 


66361 




461 


66370 


66380 


66389 


66398 


66408 


66417 


66427 


66436 


66445 


66455 




462 


66464 


66474 


66483 


66492 


66502 


66511 


66521 


66530 


66539 


66549 




463 


66558 


66567 


66577 


66586 


66596 


66605 


66614 


66624 


66633 


66642 




464 


66652 


66661 


66671 


66680 


66689 


66699 


66708 


66717 


66727 


66736 




465 


66745 


66755 


66764 


66773 


66783 


66792 


66801 


66811 


66820 


66829 




466 


66839 


66848 


66857 


66867 


66876 


66885 


66894 


66904 


66913 


66922 




467 


66932 


66941 


66950 


66960 


66969 


66978 


66987 


66997 


67006 


67015 




463 


67025 


67034 


67043 


67052 


67062 


67071 


67080 


67039 


67099 


67108 




469 


67117 


67127 


67136 


67145 


67154 


67164 


67173 


67182 


67191 


67201 




470 


67210 


67219 


67228 


67237 


67247 


67256 


67265 


67274 


67284 


67293 




471 


67302 


67311 


67321 


67330 


67339 


67348 


67357 


67367 


67376 


67385 




472 


67394 


67403 


67413 


67422 


67431 


67440 


67449 


67459 


67468 


67477 




473 


67486 


67495 


67504 


67514 


67523 


67532 


67541 


67550 


67560 


67569 




474 


67578 


67587 


67596 


67605 


67614 


67624 


67633 


67642 


67651 


67660 




475 


67669 


67679 


67688 


67697 


67706 


67715 


67724 


67733 


67742 


67752 




476 


67761 


67770 


67779 


67788 


67797 


67806 


67815 


67825 


67834 


67843 




477 


67852 


67861 


67870 


67879 


67888 


67897 


67906 


67916 


67925 


67934 




478 


67943 


67952 


67961 


67970 


67979 


67988 


67997 


68006 


68015 


68024 




479 
430 


68034 


68043 
68133 


68052 
68142 


68061 
68151 


68070 
68160 


68079 
68169 


68088 
68178 


68097 
68187 


68106 
68196 


68115 
68205 




68124 




481 


68215 


68224 


68233 


68242 


68251 


68260 


68269 


68278 


68287 


68296 




482 


68305 


68314 


68323 


68332 


68341 


68350 


68359 


68368 


68377 


68386 




483 


68395 


68404 


68413 


68422 


68431 


68440 


68449 


68458 


68467 


68476 




484 


68485 


68494 


68502 


68511 


68520 


68529 


68538 


68547 


68556 


68565 




485 


68574 


68583 


68592 


68601 


68610 


68619 


68628 


68637 


68646 


68655 




486 


68664 


68673 


68681 


68690 


68699 


68708 


68717 


68726 


68735 


68744 




437 


68753 


68762 


68771 


68780 


68789 


68797 


68806 


68815 


68824 


68833 




488 


68842 


68851 


68860 


68869 


68873 


68886 


68895 


68904 


68913 


68922 




439 
490 


68931 
69020 


68940 
69028 


68949 
69037 


68958 


68966 


68975 
69064 


68984 


68993 


69002 


69011 
69099 




69046 


69055 


69073 


69082 


69090 




491 


69108 


69117 


69126 


69135 


69144 


69152 


69161 


69170 


69179 


69188 




492 


69197 


69205 


69214 


69223 


69232 


69241 


69249 


69258 


69267 


69276 




493 


69285 


69294 


69302 


69311 


69320 


69329 


69338 


69346 


69355 


69364 




494 


69373 


69381 


69390 


69399 


69408 


69417 


69425 


69434 


69443 


69452 




495 


69461 


69469 


69478 


69487 


69496 


69504 


69513 


69522 


69531 


69539 




496 


69548 


69557 


69566 


69574 


69583 


69592 


69601 


69609 


69618 


69627 




497 


69636 


69644 


69653 


69662 


69671 


69679 


69688 


69697 


69705 


69714 




498 


69723 


69732 


69740 


69749 


69758 


69767 


69775 


69784 


69793 


69801 




499 
500 


69810 
69897 


69819 
69906 


69827 
69914 


69836 
69923 


69845 
69932 


69854 
69940 


69862 


69871 
69958 


69880 
69966 


69883 




69949 


69975; 


501 


69984 


69992 


70001 


70010 


70018 


70027 


70036 


70044 


70053 


70062 |j 


502 


70070 


70079 


70088 


70096 


70105 


70114 


70122 


70131 


70140 


70148 




503 


70157 


70165 


70174 


70183 


70191 


70200 


70209 


70217 


70226 


70234 




504 


70243 


70252 


70260 


70269 


70278 


70286 


70295 


70303 


70312 


70321 




505 


70329 


70338 


70346 


70355 


70364 


70372 


70381 


70389 


70398 


70406 




506 


70415 


70424 


70432 


70441 


70449 


70458 


70467 


70475 


70484 


70492 




507 


70501 


70509 


70518 


70526 


70535 


70544 


70552 


70561 


70569 


70578 




508 


70586 


70595 


70603 


70612 


70621 


70629 


'10638 


70646 


70655 


70663 




509 
510 


70672 

70757 


70680 


70689 
70774 


70697 
70783 


70706 
70791 


70714 
70800 


70723 
70808 


70731 
70817 


70740 
70825 


70749 




70766 


70834 




511 


70842 


70851 


70859 


70868 


70876 


70885 


70893 


70902 


70910 


70919 




512 


70927 


70935 


70944 


70952 


70961 


70969 


70978 


70986 


70995 


71003 




513 


71012 


71020 


71029 


71037 


71046 


71054 


71063 


71071 


71079 


71088 




514 


71096 


71105 


71113 


71122 


71130 


71139 


71147 


71155 


71164 


71172 




515 


71181 


71189 


71198 


71206 


71214 


71223 


71231 


71240 


71248 ! 


71257 




516 


71265 


71273 


71282 


71290 


71299 


71307 


71315 


71324 


71332 


71341 




517 


71349 


71357 


71366 


71374 


71383 


71391 


71399 


71408 


71416 


71425 




518 


71433 


71441 


71450 


71458 


71466 


71475 


71483 


71492 


71500 


71508 




1519 


71517 


71525 


71533 


71542 


71550 


71559 


71567 


71575 


71584 


71592 





100 



Logarithms from 1 to 10,000. 



No. 
520 





1 


2 


3 


4 


5 


6 




8 


9 


71600 


71609 


71617 


71625 


71634 


71642 


71650 


7ie<59 


71667 


71675 


521 


71684 


71692 


71700 


71709 


71717 


71725 


71734 


71742 


71750 


71759 


522 


71767 


71775 


71784 


71792 


71800 


71809 


71817 


71825 


71834 


71842 


523 


71850 


71858 


71867 


71875 


71883 


71892 


71900 


71908 


71917 


71925 


524 


71933 


71941 


71950 


71953 


71966 


71975 


71983 


71991 


71999 


72008 


525 


72016 


72024 


72032 


72041 


72049 


72057 


72066 


72074 


72082 


72090 


526 


72099 


72107 


72115 


72123 


72132 


72140 


72148 


72156 


72165 


72173 


527 


72181 


72189 


72198 


72206 


72214 


72222 


72230 


72239 


72247 


72255 


528 


72263 


72272 


72280 


72288 


72296 


72304 


72313 


72321 


72329 


72337 


529 
530 


72346 

72428 


72354 


72362 
72444 


72370 

72452 


72378 
72460 


72387 
72469 


72395 


72403 

72485 


72411 
72493 


72419 
72501 


72436 


72477 


531 


72509 


72518 


72526 


72534 


72542 


72550 


72558 


72567 


72575 


72583 


532 


72591 


72599 


72607 


72616 


72624 


72632 


72640 


72648 


72656 


72665 


533 


72673 


72681 


72689 


72697 


72705 


72713 


72722 


72730 


72738 


72746 


534 


72754 


72762 


72770 


72779 


72787 


72795 


72803 


72811 


72819 


72827 


535 


72835 


72843 


72852 


72860 


72868 


72876 


72884 


72892 


72900 


72908 


536 


72916 


72925 


72933 


72941 


72949 


72957 


72965 


72973 


72981 


72989 


537 


72997 


73006 


73014 


73022 


73030 


73038 


73046 


73054 


73062 


73070 


538 


73078 


73086 


73094 


73102 


73111 


73119 


73127 


73135 


73143 


73151 


539 
540 


73159 


73167 

73247 


73175 


73183 
73263 


73191 

73272 


73199 


73207 


73215 
73296 


73223 


73231 
73312 


73239 


73255 


73280 


73288 


73304 


541 


73320 


73328 


73336 


73344 


73352 


73360 


73368 


73376 


73384 


73392 


542 


73400 


73408 


73416 


73424 


73432 


73440 


73448 


73456 


73464 


73472 


543 


73480 


73488 


73496 


73504 


73512 


73520 


73528 


73536 


73544 


73552 


544 


73560 


73568 


73576 


73584 


73592 


73600 


73608 


73616 


73624 


73632 


545 


73640 


73648 


73656 


73664 


73672 


73679 


73687 


73695 


73703 


73711 


546 


73719 


73727 


73735 


73743 


73751 


73759 


73767 


73775 


73783 


73791 


547 


73799 


73807 


73815 


73823 


73830 


73838 


73846 


73854 


73862 


73870 


548 


73878 


73886 


73894 


73902 


73910 


73918 


73926 


73933 


73941 


73949 


549 
550 


73957 


73965 
74044 


73973 


73981 
74060 


73989 
74068 


73997 


74005 
74084 


74013 

74092 


74020 
74099 


74028 
74107 


74036 


74052 


74076 


551 


74115 


74123 


74131 


74139 


74147 


74155 


74162 


74170 


74178 


74186 


552 


74194 


74202 


74210 


74218 


74225 


74233 


74241 


74249 


74257 


74265 


553 


74273 


74280 


74288 


74296 


74304 


74312 


74320 


74327 


74335 


74343 


554 


74351 


74359 


74367 


74374 


74382 


74390 


74398 


74406 


74414 


74421 


555 


74429 


74437 


74445 


74453 


74461 


74468 


74476 


74484 


74492 


74500 


556 


74507 


74515 


74523 


74531 


74539 


74547 


74554 


74562 


74570 


74578 


557 


74586 


74593 


74601 


74609 


74617 


74624 


74632 


74640 


74648 


74656 


558 


74663 


74671 


74679 


74687 


74695 


74702 


74710 


74718 


74726 


74733 


559 
560 


74741 
74819 


74749 
74827 


74757 
74834 


74764 


74772 
74850 


74780 
74858 


74788 
74865 


74796 
74873 


74803 
74881 


74811 


74842 


74839 


561 


74896 


74904 


74912 


74920 


74927 


74935 


74943 


74950 


74958 


74966 


562 


74974 


74981 


74989 


74997 


75005 


75012 


75020 


75028 


75035 


75013 


563 


75051 


75059 


75066 


75074 


75082 


75089 


75097 


75105 


75113 


75120 


564 


75128 


75136 


75143 


75151 


75159 


75166 


75174 


75182 


75189 


75197 


565 


75205 


75213 


75220 


75228 


75236 


75243 


75251 


75259 


75266 


75274 


566 


75282 


75289 


75297 


75305 


75312 


75320 


75328 


75335 


75343 


75351 


567 


75358 


75366 


75374 


75381 


75389 


75397 


75404 


75412 


7M20 


75 127 


568 


75435 


75442 


75450 


75458 


75465 


75473 


75481 


75488 


75496 


75504 


, 569 
570 


75511 

75587 


75519 
75595 


75526 


75534 
75610 


75542 
75618 


75549 
75626 


75557 
75633 


75565 
75641 


75572 
75648 


75580 


75603 


75(556 


571 


75664 


75671 


75679 


75686 


75694 


75702 


75709 


75717 


75724 


75732 


572 


75740 


75747 


75755 


75762 


75770 


75778 


75785 


75793 


75800 


75808 


573 


75815 


75823 


75831 


75838 


75846 


75853 


75861 


75868 


75876 


75884 


574 


75891 


75899 


75906 


75914 


75921 


75929 


75937 


75944 


75952 


75959 


575 


75967 


75974 


75982 


75989 


75997 


76005 


76012 


76020 


76027 


76035 


576 


76042 


76050 


76057 


76065 


76072 


76080 


76087 


76095 


76103 


76110 


577 


76118 


76125 


76133 


76140 


76148 


76155 


76163 


76170 


I 76178 


76185 


57; 


1 76193 


76200 


76208 


76215 


! 76223 


76230 


76233 


1 762-45 


76253 


76260 


579 : 76 r,tt ! 76275 


! 76283 i 76290 


76298 


76305 


76313 


76320 ~ 


76335 



Logarithms from 1 to 10,000. 



101 





No. 
580 





1 


2 
76358 


3 


4 


5 


6 


7 


8 
76403 


9 






76343 


76350 


76365 


76373 


76380 


76388 


76395 


76410 






581 


76418 


76425 


76433 


76440 


76448 


76455 


76462 


76470 


76477 


76485 






582 


76492 


76500 


76507 


76515 


76522 


76530 


76537 


76545 


76552 


^6559 






583 


76567 


76574 


76582 


76589 


76597 


76604 


76612 


76619 


76626 


76634 






584 


76641 


76649 


76656 


76664 


76671 


76678 


76686 


76693 


76701 


76708 






585 


76716 


76723 


76730 


76738 


76745 


76753 


76760 


76768 


76775 


76782 






586 


76790 


76797 


76805 


76812 


76819 


76827 


76834 


76842 


76849 


76856 






587 


76864 


76871 


76879 


76886 


76893 


76901 


76908 


76916 


76923 


76930 






588 


76938 


76945 


76953 


76960 


76967 


76975 


76982 


76989 


76997 


77004 






589 
590 


77012 


77019 
77093 


77026 


77034 


77041 


77048 
77122 


77056 
77129 


77063 
77137 


77070 
77144 


77078 






77085 


77100 


77107 


77115 


77151 






591 


77159 


77166 


77173 


77181 


77188 


77195 


77203 


77210 


77217 


77225 






592 


77232 


77240 


77247 


77254 


77262 


77269 


77276 


77283 


77291 


77298 






593 


77305 


77313 


77320 


77327 


77335 


77342 


77349 


77357 


77364 


77371 






594 


77379 


77386 


77393 


77401 


77408 


77415 


77422 


77430 


77437 


77444 






595 


77452 


77459 


77466 


77474 


77481 


77488 


77495 


77503 


77510 


77517 






596 


77525 


77532 


77539 


77546 


77554 


77561 


77568 


77576 


77583 


77590 






597 


77597 


77605 


77612 


77619 


77627 


77634 


77641 


77648 


77656 


77663 






598 


77670 


77677 


77685 


77692 


77699 


77706 


77714 


77721 


77728 


77735 






599 
600 


77743 
77815 


77750 

77822 


77757 
77830 


77764 
77837 


77772 
77844 


77779 
77851 


77786 
77859 


77793 
77866 


77801 

77873 


77808 






77880 






601 


77887 


77895 


77902 


77909 


77916 


77924 


77931 


77938 


77945 


77952 






602 


77960 


77967 


77974 


77981 


77988 


77996 


78003 


78010 


78017 


78025 






603 


78032 


78039 


78046 


78053 


78061 


78068 


78075 


78082 


78089 


78097 






604 


78104 


78111 


78118 


78125 


78132 


78140 


78147 


78154 


78161 


78168 






605 


78176 


78183 


78190 


78197 


78204 


78211 


78219 


78226 


78233 


78240 






606 


7.1247 
78319 


78254 


78262 


78269 


78276 


78283 


78290 


78297 


78305 


78312 






607 


78326 


78333 


78340 


78347 


78355 


78362 


78369 


78376 


78383 






608 


78390 


78398 


78405 


78412 


78419 


78426 


78433 


78440 


78447 


78455 






609 
610 


78462 
78533 


78469 
78540 


78476 
78547 


78483 
78554 


78490 
78561 


78497 
78569 


78504 
78576 


78512 
78583 


78519 
78590 


78526 






78597 






611 


78604 


78611 


78618 


78625 


78633 


78640 


78647 


78654 


78661 


78668 






612 


78675 


78682 


78689 


78696 


78704 


78711 


78718 


78725 


78732 


78739 






613 


78746 


78753 


78760 


78767 


78774 


78781 


78789 


78796 


78803 


78810 






614 


78817 


78824 


78831 


78838 


78845 


78852 


78859 


78866 


78873 


78880 






615 


78888 


78895 


78902 


78909 


78916 


78923 


78930 


78937 


78944 


78951 






616 


78958 


78965 


78972 


78979 


78986 


78993 


79000 


79007 


79014 


79021 






617 


79029 


79036 


79043 


79050 


79057 


79064 


79071 


79078 


79085 


79092 






618 


79099 


79106 


79113 


79120 


79127 


79134 


79141 


79148 


79155 


79162 






619 
620 


79169 
79239 


79176 


79183 
79253 


79190 
79260 


79197 


79204 
79274 


79211 
79281 


79218 
79288 


79225 
79295 


79232 






79246 


79267 


79302 






621 


79309 


79316 


79323 


79330 


79337 


79344 


79351 


793/8 


79365 


79372 






622 


79379 


79386 


79393 


79400 


79407 


79414 


79421 


79428 


79435 


79442 






623 


79449 


79456 


79463 


79470 


79477 


79484 


79491 


79498 


79505 


79511 






624 


79518 


79525 


79532 


79539 


79546 


79553 


79560 


79567 


79574 


79581 






625 


79588 


79595 


79602 


79609 


79616 


79623 


79630 


79637 


79644 


79650 






626 


79657 


79664 


79671 


79678 


79685 


79692 


79699 


79706 


79713 


79720 






627 


79727 


79734 


79741 


79748 


79754 


79761 


79768 


79775 


79782 


79789 






628 


79796 


79803 


79810 


79817 


79824 


79831 


79837 


79844 


79851 


79858 






629 
630 


79865 


79872 


79879 


79886 
79955 


79893 


79900 
79969 


79906 
79975 


79913 
79982 


79920 
79989 


79927 






79934 


79941 


79948 


79962 


79996 






631 


80003 


80010 


80017 


80024 


80030 


80037 


80044 


80051 


80058 


80065 






632 


80072 


80079 


80085 


80092 


80099 


80106 


80113 


80120 


80127 


80134 






633 


80140 


80147 


80154 


80161 


80168 


80175 


80182 


80188 


80195 


80202 






634 


80209 


80216 


80223 


80229 


80236 


80243 


80250 


80257 


80264 


80271 






635 


80277 


80284 


80291 


80298 


80305 


80312 


80318 


80325 


80332 


80339 






636 


80346 


80353 


80359 


80366 


80373 


80380 


80387 


80393 


80400 


80407 






637 


80414 


80421 


80428 


80434 


80441 


80448 


80455 


80462 


80468 


80475 






;638 


80482 


80489 


80496 


80502 


80509 


80516 


80523 


80530 


80536 


80543 






639 


80550 


80557 


80564 


80570 


80577 


80584 


80591 


80598 


80604 


806T1 





ro-2 



Logarithms from 1 to 10,000. 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


640 


80618 


80625 


80632 


80638 


80645 


80652 


80659 


80665 


80672 


80679 


641 


80686 


80693 


80699 


80706 


80713 


80720 


80726 


80733 


80740 


80747 


642 


80754 


80760 


80767 


80774 


80781 


80787 


80794 


80801 


80808 


80814 


643 


80821 


80828 


80835 


80841 


80848 


80855 


80862 


80868 


80875 


80882 


644 


80889 


80895 


80902 


80909 


80916 


80922 


80929 


80936 


80943 


80949 


645 


80956 


80963 


80969 


80976 


80983 


80990 


80996 


81003 


81010 


81017 


646 


SI 023 


81030 


81037 


81043 


31050 


81057 


81064 


81070 


81077 


81084 


647 


81090 


81097 


81104 


81111 


81117 


81124 


81131 


81137 


81144 


81151 


648 


81158 


81164 


81171 


81178 


81184 


81101 


81198 


81204 


81211 


81218 


649 
650 


81224 
81291 


81231 

81298 


81238 


81245 


81251 


81258 


81265 
81331 


81271 
81338 


81278 
81345 


81285 
81351 


81305 


81311 


81318 


81325 


651 


81358 


81365 


81371 


81378 


81385 


81391 


81398 


81405 


81411 


81418 


652 


81425 


81431 


81438 


81445 


81451 


81458 


81465 


81471 


81478 


81485 


653 


81491 


81498 


81505 


81511 


81518 


81525 


81531 


81533 


81544 


81551 


654 


81558 


81564 


81571 


81578 


81584 


81591 


81598 


81604 


81611 


81617 


655 


81624 


81631 


81637 


81644 


81651 


81657 


81664 


81671 


81677 


81684 


656 


81690 


81697 


81704 


81710 


81717 


81723 


81730 


81737 


81743 


81750 


657 


81757 


81763 


81770 


81776 


81783 


81790 


81796 


81803 


81809 


81816 


653 


31823 


81829 


81836 


81842 


81849 


81856 


81862 


81869 


81875 


81882 


659 
660 


81889 
81954 


81895 


81902 


81908 
31974 


81915 


81921 
81987 


81928 
81994 


81935 
82000 


81941 
82007 


81948 
82014 


31961 


81968 


81981 


661 


82020 


82027 


82033 


82040 


82046 


82053 


82060 


82066 


82073 


82079 


662 


82086 


82092 


82099 


82105 


82112 


82119 


82125 


82132 


82138 


82145 


663 


82151 


82158 


82164 


82171 


82178 


82184 


82191 


82197 


82204 


82810 


664 


82217 


82223 


82230 


82236 


82243 


82240 


82256 


82263 


82269 


82276 


665 


82282 


82289 


82205 


82302 


82308 


82315 


82321 


82328 


82334 


82341 . 


666 


82347 


82354 


82360 


82367 


82373 


82380 


82387 


82393 


82400 


82406 


667 


82413 


82419 


82426 


82432 


82439 


82445 


82452 


82458 


82465 


82471 


663 


82478 


82484 


82401 


82497 


82504 


82510 


82517 


82523 


82530 


82536 


669 
670 


82543 
82607 


82549 
82614 


82556 


82562 


82569 


82575 
82640 


82582 
82646 


82588 


82595 
82659 


82601 
82666 


82620 


82627 


82633 


82653 


671 


82672 


82679 


82685 


82692 


82698 


82705 


82711 


82718 


82724 


82730 


672 


82737 


82743 


82750 


82756 


82763 


82769 


82776 


82782 


82789 


82795 


673 


82802 


82808 


82814 


82821 


82827 


82834 


82840 


82847 


82853 


82860 


674 


82866 


82872 


82879 


82885 


82892 


82898 


82905 


82911 


82918 


82924 


675 


82930 


82937 


82943 


82950 


82956 


82963 


82969 


82975 


82982 


82988 


676 


82995 


83001 


83008 


83014 


83020 


83027 


83033 


83040 


83046 


83052 


677 


83059 


83065 


83072 


83078 


83085 


83091 


83097 


83104 


83110 


83117 


678 


83123 


83129 


83136 


83142 


83149 


83155 


83161 


83168 


83174 


83181 


679 
680 


83187 
83251 


83193 
83257 


83200 
83264 


83206 
83270 


83213 


83219 


83225 
83289 


83232 


83238 
83302 


83245 


83276 


83283 


83296 


83308 


631 


83315 


83321 


83327 


83334 


83340 


83347 


83353 


83359 


83366 


83372 


1682 


83378 


83385 


83391 


83398 


83404 


83410 


83417 


83423 


83429 


83436 


683 


83442 


83448 


83455 


83461 


83467 


83474 


83480 


83487 


83493 


83499 


684 


83506 


83512 


83518 


83525 


83531 


83537 


83544 


83550 


83556 


83563 


685 


83569 


83575 


83582 


83583 


83594 


83601 


83607 


83613 


83620 


83626 


686 


83632 


83639 


83645 


83651 


83653 


83664 


83670 


83677 


83683 


83689 


687 


83696 


83702 


83708 


83715 


83721 


83727 


83734 


83740 


83746 


83753 


688 


83759 


83765 


83771 


83778 


83784 


83790 


83797 


83803 


83809 


83816 


689 
690 


83822 
83885 


83828 
83891 


83835 
83397 


83841 


83847 
83910 


83853 
83916 


83860 
83923 


83366 


83872 
83935 


83879 


83904 


83929 


83942 


691 


83948 


83954 


83960 


83967 


83973 


83979 


83985 


83992 


83998 1 


84004 


692 


84011 


84017 


84023 


84029 


84036 


84042 


84048 


84055 


84061 


84067 


693 


84073 


84080 


84086 


84092 


84098 


84105 


84111 j 


84117 


84123 


84130 


694 


84136 


84142 


84148 


84155 


84161 


84167 


84173 


84180 


84186 


84192 


695 


84198 


84205 


84211 


84217 


84223 


84230 


84236 


8-1242 


84248 


84255 


696 


84261 


84267 


84273 


84280 


84286 


84292 


84298 j 


84305 


84311 


84317 


697 


84323 


84330 


84336 


84342 


84348 


84354 


84361 1 


84367 


84373 


84379 


698 


84386 


84392 


84398 


84404 84410 


84417 


84423 


84429 


84435 


84442 


699 


84448 


84454 


84460 


84466 1 84473 1 84479 


84485 1 


84491 


84497 


84504 



Logarithms from 1 to 10,000. 



103 



.No. 



84510 

84572 
84634 
84696 
84757 
84819 

706 84880 

707 84942 

708 85003 

709 85065 
710 
711 
712 
713 
714 
715 
716 
717 
718 
719 
720 
721 
7-2-2 
723 
724 



85126 
85187 
85248 
85309 
85370 
85431 
85491 
85552 
85612 
85673 



85733 
85794 
85854 
85914 
85974 
86034 
86094 



727 


86153 


728 


86213 


729 


86273 


730 


86332 


731 


86392 


732 


86451 


733 


86510 


734 


86570 


735 


86629 


736 


86688 


737 


86747 


738 


86806 


739 


86864 



85132 
85193 
85254 
85315 
85376 
85437 
85497 
85558 
85618 
85679 



740 


86923 


741 


86982 


742 


87040 


743 


87099 


744 


87157 


745 


87216 


746 


87274 


747 


87332 


748 


87390 


749 


87448 


750 


87506 


751 


87564 


752 


87622 


753 


87679 


754 


87737 


755 


87795 


756 


87852 


757 


87910 


758 


87967 


759 


88024 



85739 
85800 
85860 
85920 
85980 
86040 
86100 
86159 
86219 
86279 



86338 
86398 
86457 
86516 
86576 
86635 
86694 
86753 
86812 
86870 



86929 
86988 
87046 
87105 
87163 
87221 
87280 
87338 
87396 
87454 



2 


3 


84522 


84528 


84584 


84590 


84646 


84652 


84708 


84714 


84770 


84776 


84831 


84837 


84893 


84899 


84954 


84960 


85016 


85022 


85077 


85083 


85138 


85144 


85199 


85205 


85260 


85266 


85321 


85327 


85382 


85388 


85443 


85449 


85503 


85509 


85564 


85570 


85625 


85631 


85685 


85691 


85745 


85751 


85806 


85812 


85866 


85872 


85926 


85932 


85986 


85992 


86046 


86052 



87512 
87570 
87628 
87685 
87743 
87800 
87858 
87915 
87973 
88030 



86106 
86165 
86225 



86344 
86404 
86463 
86522 
86581 
86641 
86700 
86759 
868)7 
86876 



86935 
86994 
87052 
87111 
87169 
87227 
87286 
87344 
87402 
87460 



87518 
87576 
87633 
87691 
87749 
87806 
87864 
87921 
87978 
88036 



86112 
86171 
86231 
86291 



86350 
86410 
86469 
86528 



86646 
86705 
86764 
86823 
86882 



84535 
84597 
84658 
84720 
84782 
84844 
84905 
84967 
85028 
85089 
85150 
85211 
85272 
85333 
85394 
85455 
85516 
85576 
85637 
85697 



86999 
87058 
87116 
87175 
87233 
87291 
87349 
87408 
87466 
87523 
87581 
87639 
87697 
87754 
87812 



87927 
87984 
88041 



85757 
85818 
85878 
85938 
85998 
86058 
86118 
86177 
86237 



84541 
84603 
84665 
84726 
84788 
84850 
84911 
84973 
85034 
85095 



86356 
86415 
86475 
86534 
86593 
86652 
86711 
86770 
86829 



86947 
87005 
87064 
87122 
87181 
87239 
87297 
87355 
87413 
87471 



87529 
87587 
87645 
87703 
87760 
87818 
87875 
87933 
87990 
88047 



85156 
85217 
85278 
85339 
85400 
85461 
85522 
85582 
85643 
85703 



84547 
84609 
84671 
84733 
84794 
84856 
84917 
84979 
85040 
85101 
85163 
85224 
85285 
85345 
85406 
85467 
85528 
85588 
85649 
85709 



85763 
85824 
85884 
85944 
86004 
86064 
86124 
86183 
86243 
86303 



86362 
86421 
86481 
86540 
86599 



86717 
86776 
86835 
86894 



87011 
87070 
87128 
87186 
87245 
87303 
87361 
87419 
87477 



87535 
87593 
87651 
87708 
87766 
87823 
87881 
87938 
87996 
88053 



85769 
85830 
85890 
85950 
86010 
86070 
86130 
86189 
86249 



86368 
86427 
86487 
86546 
86605 
86664 
86723 
86782 
86841 
86900 



87017 
87075 
87134 
87192 
87251 
87309 
87367 
87425 
87483 



84553 
84615 
84677 
84739 
84800 
84862 
84924 
84985 
85046 
85107 
85169 
85230 
85291 
85352 
85412 
85473 
85534 
85594 
85655 
85715 



87541 
87599 
87656 
87714 
87772 
87829 
87887 
87944 
88001 
88058 



84559 

84621 

84683 

84745 

84807 

84868 

84930 

84991 

| 85052 

1 85114 

I 85175 

j 85236 

85297 

85358 

85418 

j 85479 

85540 

| 85600 

85661 

85721 



85775 
85836 
85896 
85956 
86016 
86076 
86136 
86195 
86255 
86314 



86374 
86433 
86493 
86552 
86611 
86670 
86729 
86788 
86847 



86964 
87023 
87081 
87140 
87198 
87256 
87315 
87373 
87431 
87489 



87547 
87604 



87720 
87777 
87835 
87892 
87950 
88007 
88064 



85781 
85842 
85902 



86022 
86082 
86141 
86201 
86261 
86320 



86380 
86439 
86499 
86558 
86617 
86676 
86735 
86794 
86853 
86911 



86970 
87029 
87087 
87146 
87204 
87262 
87320 
87379 
87437 
87495 



84566 
84628 
84689 
84751 
84813 
84874 
84936 
84997 
85058 
85120 



87552 
87610 
87668 
87726 
87783 
87841 



87955 
88013 
88070 



85181 

85242 

85303 I 

85364 ! 

8542£ 

85485 j 

85546 \ 

85606 i 

85667 

85727 

85788 

8584[ 

85908 

85968 

86028! 

86088 i 

86147 

86207 | 

86267! 

86326 I 

86386 



8644 



:) 



:: 



86504 

86564 

866 

866821 

86741 | 

86800 : 

86850 

8691 7. 

86976 ; 

87035 

87003 

87151! 

872 1 

87268- 

87326 j 

87384 ; 

87442, 

87500 j 

87558 

87616 

87674 

87731 

87789 

87846 

87904 

87961 

88018 

88076 



104 



Logarithms from 1 to 10,000. 



No. 
760 





1 


2 


3 


4 


5 


6 


7 


8 


9 




88081 


8808^ 


88093 


88098 


88104 


88110 


88116 


88121 


88127 


88133 




761 


88138 


88144 


88150 


88156 


88161 


88167 


88173 


88178 


88184 


88190 




762 


88195 


88201 


88207 


88213 


88218 


88224 


88230 


88235 


88241 


88247 




763 


88252 


88258 


88264 


88270 


88275 


88281 


88287 


88292 


88298 


88304 




764 


88309 


88315 


88321 


88326 


88332 


88338 


88343 


88349 


88355 


88360 




765 


88366 


88372 


88377 


88383 


88389 


88395 


88400 


88406 


88412 


88417 




766 


88423 


88429 


88434 


88440 


88446 


88451 


88457 


88463 


88468 


88474 




7«7 


88480 


88485 


88491 


88497 


88502 


88508 


88513 


88519 


88525 


88530 




768 


88536 


88542 


88547 


88553 


88559 


88564 


88570 


88576 


88581 


88587 




769 
770 


88593 
88649 


88598 
88655 


88604 
88660 


88610 


88615 
88672 


88621 
88677 


88627 
88683 


88632 


88638 


88643 




88666 


88689 


88694 


88700 




771 


88705 


88711 


88717 


88722 


88728 


88734 


88739 


88745 


88750 


88756 




772 


88762 


88767 


88773 


88779 


88784 


88790 


88795 


88801 


88807 


88812 




773 


88818 


88824 


88829 


88835 


88840 


88846 


88852 


88857 


88863 


88868 




774 


88874 


88880 


88885 


88891 


38897 


88902 


88908 


88913 


88919 


88925 




775 


88930 


88936 


88941 


88947 


88953 


88958 


88964 


88969 


88975 


88981 




776 


88986 


88992 


88997 


89003 


89009 


89014 


89020 


89025 


89031 


89037 




777 


89042 


89048 


89053 


89059 


89064 


89070 


89076 


89081 


89087 


89092 




778 


89098 


89104 


89109 


89115 


89120 


89126 


89131 


89137 


89143 


89148 




779 
780 


89154 
89209 


89159 
89215 


89165 
89221 


89170 
89226 


89176 
89232 


89182 


89187 
89243 


89193 


89198 
89254 


89204 
89260 




89237 


89248 




781 


89265 


89271 


89276 


89282 


89287 


89293 


89298 


89304 


89310 


89315 




782 


89321 


89326 


89332 


89337 


89343 


89348 


89354 


89360 


89365 


89371 




783 


89376 


89382 


89387 


89393 


89398 


89404 


89409 


89415 


89421 


89426 




784 


89432 


89437 


89443 


89448 


89454 


89459 


89465 


89470 


89476 


89481 




785 


89487 


89492 


89498 


89504 


89509 


89515 


89520 


89526 


89531 


89537 




786 


89542 


89548 


89553 


89559 


89564 


89570 


89575 


89581 


89586 


89592 




787 


89597 


89603 


89609 


89614 


89620 


89625 


89631 


89636 


89642 


89647 




788 


89653 


89658 


89664 


89669 


89675 


89680 


89686 


89691 


89697 


89702 




789 


89708 


89713 


89719 


89724 


89730 


89735 


89741 


89746 


89752 


89757 




790 


89763 


89768 


89774 


89779 


89785 


89790 


89796 


89801 


89807 


89812 




791 


89818 


89823 


89829 


89834 


89840 


89845 


89851 


89856 


89862 


89867 




792 


89873 


89878 


89883 


89889 


89894 


89900 


89905 


89911 


89916 


89922 




793 


89927 


89933 


89938 


89944 


89949 


89955 


89960 


89966 


89971 


89977 




794 


89982 


89988 


89993 


89998 


90004 


90009 


90015 


90020 


90026 


90031 




795 


90037 


90042 


90048 


90053 


90059 


90064 


90069 


90075 


90080 


90086 




796 


90091 


90097 


90102 


90108 


90113 


90119 


90124 


90129 


90135 


90140 




797 


90146 


90151 


90157 


90162 


90168 


90173 


90179 


90184 


90189 


90195 




798 


90200 


90206 


90211 


90217 


90222 


90227 


90233 


90238 


90244 






799 
800 


90255 
90309 


90260 
90314 


90266 
90320 


90271 
90325 


90276 
90331 


90282 
90336 


90287 


90293 
90347 


90298 
90352 


90304 
90358 




90342 




801 


90363 


90369 


90374 


90380 


90385 


90390 


90396 


90401 


90407 


90412 




802 


90417 


90423 


90428 


90434 


90439 


90445 


90450 


90455 


90461 


90466 




803 


90472 


90477 


90482 


90488 


90493 


90499 


90504 


90509 


90515 






804 


90526 


90531 


90536 


90542 


90547 


90553 


90558 


90563 


90569 


9057. 1 




805 


90580 


90585 


90590 


90596 


90601 


90607 


90612 


90617 


90623 


90628 




806 


90634 


90639 


90644 


90650 


90655 


90660 


90666 


90671 


90677 


90682 




807 


90687 


90693 


90698 


90703 


90709 


90714 


90720 


90725 


90730 


90736 




808 


90741 


90747 


90752 


90757 


90763 


90768 


90773 


90779 


90784 


90789 




809 
8K) 


90795 
90849 


90800 
90854 


90806 


90811 
90865 


90816 
90870 


90822 
90875 


90827 
90881 


90832 
90886 


90838 


90897 




90859 


90891 




811 


90902 


90907 


90913 


90918 


90924 


90929 


90934 


90940 


90945 


90950 




812 


90956 


90961 


90966 


90972 


90977 


90982 


90988 


90993 


90998 


91004 




813 


91009 


91014 


91020 


91025 


91030 


91036 


91041 


91046 


91052 


91057 




814 


91062 


91068 


91073 


91078 


91084 


91089 


91094 


91100 


91105 


91110J 




815 


91116 


91121 


91126 


91132 


91137 


91142 


91148 


91153 


91158 


91164 




816 


91169 


91174 


91180 


91185 


91190 


91196 


91201 


91206 


91212 


91217 




817 


91222 


91228 


91233 


91238 


91243 


91249 


91254 


91259 


91265 


91270 




818 


91275 


91281 


91286 


91291 


91297 


91302 


91307 


91312 


91318 


91323 




819 


91328 


91334 


91339 I 91344 


91350 


91355 91360 91365 


91371 


91376, 





Logarithms from I to 10,000. 



\0b 



No. 

820 
8.21 

82.2 
| &13 
I 824 
1825 

j 827 

828 
829 
830 
831 
832 
833 
834 
835 
836 
837 
838 
839 
840 
841 
842 
843 
844 
845 
846 
847 
848 
849 
850 
851 
85.2 
853 
854 
855 
856 
857 
858 
859 
860 
861 
862 
863 
864 
865 
866 
867 
868 
869 
870 
871 
872 
873 
874 
815 
876 
877 
878 
879 






2 


2 


91381 
91434 
91487 
91540 
91593 
91645 
91698 
91751 
91803 
91855 
91908 
91960 
9.2012 
92065 
92117 
92169 
92221 
92273 
92324 
92376 
92428 
92480 
92531 
92583 
92634 
92686 
92737 
92788 
92840 
92891 
92942 
92993 
93044 
93095 
93146 
93197 
93247 
93298 
93349 
93399 
93450 
93500 
93551 
93601 
93651 
93702 
93752 
93802 
93852 
93902 
93952 
94002 
94052 
94101 
94151 
94201 
94250 
94300 
94349 
94399 


91387 
91440 
91492 
91545 
91598 
91651 
91703 
91756 
91808 
91861 
91913 
91965 
92018 
92070 
92122 
92174 
92226 
92278 
92330 
92381 
92433 
92485 
92536 
92588 
92639 
92691 
92742 
92793 
92845 
92896 
92947 
92998 
93049 
93100 
93151 
93202 
93252 
93303 
93354 
93404 
93455 
93505 
93556 
93606 
93656 
93707 
93757 
93807 
93857 
93907 
93957 
94007 
94057 
94106 
94156 
94206 
94255 
94305 
94354 
94404 


91392 
91445 
91498 
91551 
91603 
91656 
91709 
91761 
91814 
91866 
91918 
91971 
92023 
92075 
92127 
92179 
92231 
92283 
92335 
92387 
92438 
92490 
92542 
92593 
92645 
92696 
92747 
92799 
92850 
92901 
92952 
93003 
93054 
93105 
93156 
93207 
93258 
93308 
93359 
93409 
93460 
93510 
93561 
93611 
93661 
93712 
93762 
93812 
93862 
93912 


93962 
94012 
94062 
94111 
94161 
94211 
94260 
94310 
94359 
94409 



91397 
91450 
91503 
91556 



91661 
91714 
91766 
91819 
91871 



91924 
91976 
92028 
92080 
92132 
92184 
92236 
92288 
92340 
92392 



92443 
92495 
92547 
92598 
92650 
92701 
92752 



92855 
92906 



92957 
93008 
93059 
93110 
93161 
93212 
93263 
93313 
93364 
93414 



93465 
93515 
93566 
93616 



93717 
93767 
93817 



93917 



93967 
94017 
94067 
94116 
94166 
94216 
94265 
94315 
94364 
94414 



91403 
91455 
91508 
91561 
91614 
91666 
91719 
91772 
91824 
91876 



91929 
91981 
92033 
92085 
92137 
92189 
92241 
92293 
92345 
92397 



92449 
92500 
92552 
92603 
92655 
92706 
92758 
92809 
92860 
92911 



93013 
93064 
93115 
93166 
93217 
93268 
93318 
93369 
93420 



93470 
93520 
93571 
93621 
93671 
93722 
93772 
93822 
93872 
93922 



93972 
94022 
94072 
94121 
94171 
94221 
94270 
94320 
94369 
94419 



91408 
91461 
91514 
91566 
91619 
91672 
91724 
91777 
91829 
91882 



91934 



92091 
92143 
92195 
92247 
92298 
92350 
92402 



92454 
92505 
92557 
92609 
9.2660 
92711 
92763 
92814 
92865 
92916 
92967 
93018 
93069 
93120 
93171 
93222 
93273 
93323 
93374 
93425 



93475 
93526 
93576 
93626 
93676 
93727 
93777 
93827 
93877 
93927 



93977 
94027 
94077 
94126 
94176 
94226 
94275 
94325 
94374 
94424 



91413 
91466 
91519 
91572 
91624 
91677 
91730 
91782 
91834 
91887 



91939 



92044 
92096 
92148 
92200 
92252 
92304 
92355 
92407 



92459 
92511 
92562 
92614 
92665 
92716 
92768 
92819 
92870 
92921 



92973 
93024 
93075 
93125 
93176 
93227 
93278 
93328 
93379 
93430 



93480 
93531 
93581 
93631 
93682 
93732 
93782 
93832 
93882 
93932 



93982 
94032 
94082 
94131 
94181 
94231 
94280 
94330 
94379 
94429 



91418 
91471 
91524 
31577 
91630 



91735 
91787 
91840 



91944 
91997 
92049 
92101 
92153 
92205 



92309 
92361 
92412 



92464 
92516 
92567 
92619 
92670 
92722 
92773 
92824 
92875 
92927 



92978 
93029 
93080 
93131 
93181 
93232 
93283 
93334 
93384 
93435 



93485 
93536 
93586 
93636 
93687 
93737 
93787 
93837 
93887 
93937 



93987 
94037 



94136 
94186 
94236 
94285 
94335 
94384 
94433 



91424 
91477 
91529 
91582 
91635 
91687 
91740 
91793 
91845 
91897 



91950 
92002 
92054 
92106 
92158 
92210 
92262 
92314 



92418 



92469 
92521 
92572 
926.24 
92675 
92727 
92778 
92829 
92881 



92983 
93034 
93085 
93136 
93186 
93237 
93288 
93339 
93389 
93440 



93490 
93541 
93591 
93641 
93692 
93742 
93792 
93842 
93892 
93942 



93992 
94042 
94091 
94141 
94191 
94240 
94290 
94340 
94389 
94438 



91429 

91482 

91535 

91587 

91640 

91693 

91745 

91798 

91850 

91903 

91955 

92007 

92059 

92111 

92163 

92215 

92267 

92319 

92371 

92423 

92474 

92526 

92578 

92629 

92681 

92732 

92783 

92834 

92886 

92937 

92988 

93039 

93090 

93141 

93192 

93242 

93293 

93344 

93394 

93445 

93495 

93546 

93596 

93646 

9369^ 

93747 

93797 

9384T 

93897 

93947 

93997 

94047 

94096 

94146 

941J 

94245 

94295 

94345 

94394 

94443 



33 



30 



106 



Logarithms from 1 to 10,000. 



No. 
880 





1 


2 


3 


4 


5 


6 

94478 


7 


8 


9 




94448 


94453 


94458 


94463 


94468 


94473 


94483 


94488 


94-19.5 




881 


94498 


94503 


94507 


94512 


94517 


94522 


94527 


94532 


94537 


94542 




882 


94547 


94552 


94557 


94562 


94567 


94571 


94576 


94581 


94586 


9459 1 




883 


94596 


94601 


94606 


94611 


94616 


94621 


94626 


94630 


94635 


94640 




884 


94645 


94650 


94655 


94660 


94G65 


94670 


94675 


94680 


94685 


94689 




885 


94694 


94699 


94704 


94709 


94714 


94719 


94724 


94729 


94734 


947:;;; 




886 


94743 


94748 


94753 


94758 


94763 


94768 


94773 


94778 


94783 


94787 




887 


94792 


94797 


94802 


94807 


94812 


94817 


94822 


94827 


94832 


94836 




888 


94841 


94846 


94851 


94856 


94861 


94866 


94871 


94876 


94880 


94886 




889 


94890 


94895 


94900 


94905 


94910 


94915 


94919 


94924 


94929 


94934 




890 


94939 


94944 


94949 


94954 


94959 


94903 


94968 


94973 


94978 


94983 




891 


94988 


94993 


94998 


95002 


95007 


95012 


95017 


95022 


95027 


95032 




892 


95036 


95041 


95046 


95051 


95056 


95061 


95066 


95071 


95075 


95080 




893 


95085 


95090 


95095 


95100 


95105 


95109 


95114 


95119 


95124 


95129 




894 


95134 


95139 


95143 


95148 


95153 


95158 


95163 


95168 


95173 


95177 




895 


95182 


95187 


95192 


95197 


95202 


95207 


95211 


95216 


96221 


95226 




896 


95231 


95236 


95240 


95245 


95250 


95255 


95260 


95265 


95270 


95274 




897 


95279 


95284 


95289 


95294 


95299 


95303 


95308 


95313 


95318 


95323 




898 


95328 


95332 


95337 


95342 


95347 


95352 


95357 


95361 


95366 


95371 




899 


95376 


95381 


95386 


95390 


95395 


95400 


95405 


95410 


95415 


95419 




900 


95424 


95429 


95434 


95439 


95444 


95448 


95453 


95458 


95463 


95468 




901 


95472 


95477 


95482 


95487 


95492 


95497 


95501 


95506 


95511 


95516 




902 


95521 


95525 


95530 


95535 


95540 


95545 


95550 


95554 


95559 


95564 




903 


95569 


95574 


95578 


95583 


95588 


95593 


95598 


95602 


95607 


95612 




904 


95617 


95622 


95626 


95631 


95636 


95641 


95646 


95650 


95655 


95660 




905 


95665 


95670 


95674 


95679 


95684 


95689 


95694 


95698 


95703 


95708 




906 


95713 


95718 


95722 


95727 


95732 


95737 


95742 


95746 


95751 


95756 




907 


95761 


95766 


95770 


95775 


95780 


95785 


95789 


95794 


95799 


95804 




908 


95809 


95813 


95818 


95823 


95828 


95832 


95837 


95842 


95847 


95C52 




909 


95856 


95861 


95866 


95871 


95875 


95880 


95885 


95890 


95895 


95899 




910 


95904 


95909 


95914 


95918 


95923 


95928 


95933 


95938 


95942 


95947 




911 


95952 


95957 


95961 


95966 


95971 


95976 


95980 


95985 


95990 


9599r, 




912 


95999 


96004 


96009 


96014 


96019 


96023 


96028 


96033 


96038 


96042 




913 


96047 


96052 


96057 


96061 


96066 


96071 


96076 


96080 


96085 


96090 




914 


96095 


96099 


96104 


96109 


96114 


96118 


96123 


96128 


96133 


96137 




915 


96142 


96147 


96152 


96156 


96161 


96166 


96171 


96175 


96180 


96185 




916 


96190 


96194 


96199 


96204 


96209 


96213 


96218 


96223 


96227 


96232 




917 


96237 


96242 


96246 


96251 


96256 


96261 


96265 


96270 


96275 


96280 




918 


96284 


96289 


96294 


96298 


96303 


96308 


96313 


96317 


96322 


96327 




919 


96332 


96336 


96341 


96346 


96350 


96355 


96360 


96365 


96369 


96374 




920 


96379 


96384 


96388 


96393 


96398 


96402 


96407 


96412 


96417 


96421 




921 


96426 


96431 


96435 


96440 


96445 


96450 


96454 


96459 


96464 


96468 




. 922 


96473 


96478 


96483 


96487 


96492 


96497 


96501 


9650C 


96511 


96515 




923 


96520 


96525 


96530 


96534 


96539 


96544 


96548 


96553 


96558 


96569 




924 


96567 


96572 


96577 


96581 


96586 


96591 


96595 


96600 


96605 


96609 




925 


96614 


96619 


96624 


96628 


96633 


96638 


96642 


96647 


96652 


96658 




926 


96661 


96666 


96670 


96675 


96680 


96685 


96689 


96694 


96699 


96703 




927 


96708 


96713 


96717 


96722 


96727 


96731 


96736 


96741 


96745 


96750 




928 


96755 


96759 


96764 


96769 


96774 


96778 


96783 


96788 


96792 


96797 




929 
930 


96802 
96848 


96806 


96811 
96858 


96816 
96862 


96820 
96867 


96825 
96872 


96830 
96876 


96834 
96881 


96839 
96886 


96844 
96890 




96853 




931 


96895 


96900 


96904 


96909 


96914 


96918 


96923 


96928 


96932 


96937 




932 


96942 


96946 


96951 


96956 


96960 


96965 


96970 


96974 


96979 


96984 




933 


96988 


96993 


96997 


97002 


97007 


97011 


97016 


97021 


97025 


97030 




934 


97035 


97039 


97044 


97049 


97053 


97058 


97063 


97067 


97072 


97077 




935 


97081 


97086 


97090 


97095 


97100 


97104 


97109 


97114 


97118 


97123 




936 


97128 


97132 


97137 


97142 


97146 


9715T 


97155 


97160 


97165 


97169 




937 


97174 


97179 


97183 


97188 


97192 


97197 


97202 


97206 


97211 


97216 




938 


97220 


97225 


97230 


97234 


97239 


97243 


97248 


97253 


97257 


97262 




939 


97267 


97271 


97276 


97280 


97285 


97290 


97294 


97299 


97304 


97308 





Logarithms from 1 to 10,000. 



107 



No. 
940 





1 


2 
97322 


3 


4 


5 


6 


7 


8 


9 
97354 


97313 


97317 


97327 


97331 


97336 


97340 


97345 


97350 


941 


97359 


97364 


97368 


97373 


97377 


97382 


97387 


97391 


97396 


97400 


942 


97405 


97410 


97414 


97419 


97424 


97428 


97433 


97437 


97442 


97447 


943 


97451 


97456 


97460 


97465 


97470 


97474 


97479 


97483 


97488 


97493 . 


944 


97497 


97502 


97506 


97511 


97516 


97520 


97525 


97529 


97534 


97539 


945 


97543 


97548 


97552 


97557 


97562 


97566 


97571 


97575 


97580 


97585 


946 


97589 


97594 


97598 


97603 


97607 


97612 


97617 


97621 


97626 


97630 j 


947 


97635 


97640 


97644 


97649 


97653 


97658 


97663 


97667 


97672 


97676 | 


948 


97681 


97685 


97690 


97695 


97699 


97704 


97708 


97713 


97717 


97722 


949 
950 


97727 


97731 


97736 


97740 


97745 
97791 


97749 


97754 
97800 


97759 
97804 


97763 
97809 


97768 1 
97813! 


97772 


97777 


97782 


97786 


97795 


951 


97818 


97823 


97827 


97832 


97836 


97841 


97845 


97850 


97855 


97859 


952 


97864 


97868 


97873 


97877 


97882 


97886 


97891 


97896 


97900 


97905 


953 


97909 


97914 


97918 


97923 


97928 


97932 


97937 


97941 


97946 


97950 


954 


97955 


97959 


97964 


97968 


97973 


97978 


97982 


97987 


97991 


97996 


955 


98000 


98005 


98009 


98014 


98019 


98023 


98028 


98032 


98037 


98041 


956 


98046 


98050 


98055 


98059 


98064 


98068 


98073 


98078 


98082 


98087 


957 


98091 


98096 


98100 


98105 


98109 


98114 


98118 


98123 


98127 


98132 


958 


98137 


98141 


98146 


98150 


98155 


98159 


98164 


98168 


93173 


98177 


959 
960 


98182 
98227 


98186 
98232 


98191 


98195 
98241 


98200 
98245 


98204 
98250 


98209 
98254 


98214 
98259 


98218 
98263 


98223 
98268 


98236 


961 


98272 


98277 


98281 


98286 


98290 


98295 


98299 


98304 


98308 


98313 


962 


98318 


98322 


98327 


98331 


98336 


98340 


98345 


98349 


98354 


98358 


963 


98363 


98367 


98372 


98376 


98381 


98385 


98390 


98394 


98399 


98403 


964 


98408 


98412 


98417 


98421 


98426 


98430 


98435 


98439 


98444 


98448 • 


965 


98453 


98457 


98462 


98466 


98471 


98475 


98480 


98484 


98489 


98493 1 


966 


98498 


98502 


98507 


98511 


98516 


98520 


98525 


98529 


98534 


98538 


967 


98543 


98547 


98552 


98556 


98561 


98565 


98570 


98574 


98579 


98583 


968 


98588 


98592 


98597 


98601 


98605 


98610 


98614 


98619 


98623 


98628 


969 
970 


98632 


98637 
98682 


98641 
98686 


98646 
98691 


98650 
98695 


98655 
98700 


98659 
98704 


98664 
98709 


98668 
98713 


98673 
98717 


98677 


971 


98722 


98726 


98731 


98735 


98740 


98744 


98749 


98753 


98758 


987621 


972 


98767 


98771 


98776 


98780 


98784 


98789 


98793 


98798 


98802 


98807 


973 


98811 


98816 


98820 


98825 


98829 


98834 


98838 


98843 


98847 


98851 


974 


98856 


98860 


98865 


98869 


98874 


98878 


98883 


98887 


98892 


98896 


975 


98900 


98905 


98909 


98914 


98918 


98923 


98927 


98932 


98936 


98941 


976 


98945 


98949 


98954 


98958 


98963 


98967 


98972 


98976 


98981 


98985 


977 


98989 


98994 


98998 


99003 


99007 


99012 


99016 


99021 


99025 


99029 


978 


99034 


99038 


99043 


99047 


99052 


99056 


99061 


99065 


99069 


99074 


979 
980 


99078 


99083 


99087 
99131 


99092 
99136 


99096 


99100 
99145 


99105 
99149 


99109 


99114 
99158 


99118 
99162 


99123 


99127 


99140 


99154 


981 


99167 


99171 


99176 


99180 


99185 


99189 


99193 


99198 


99202 


99207 


982 


99211 


99216 


99220 


99224 


99229 


99233 


99238 


99242 


99247 


99251 


983 


99255 


99260 


99264 


99269 


99273 


99277 


99282 


99286 


99291 


99295 


984 


99300 


99304 


99308 


99313 


99317 


99322 


99326 


99330 


99335 


99339 


985 


99344 


99348 


99352 


99357 


99361 


99366 


99370 


99374 


99379 


99383 


986 


99388 


99392 


99396 


99401 


99405 


99410 


99414 


99419 


99423 


99427 


987 


99432 


99436 


99441 


99445 


99449 


99454 


99458 


99463 


99467 


99471 


988 


99476 


99480 


99484 


99489 


99493 


99498 


99502 


99506 


99511 


99515 


989 
990 


99520 
99564 


99524 


99528 
99572 


99533 

99577 


99537 
99581 


99542 
99585 


99546 
99590 


99550 


99555 


99559 
99603 


99568 


99594 


99599 


991 


99607 


99612 


99616 


99621 


99625 


99629 


99634 


99638 


99642 


99647 


992 


99651 


99656 


99660 


99664 


99669 


99673 


99677 


99682 


99686 


99691 


993 


99695 


99699 


99704 


99708 


99712 


99717 


99721 


99726 


99730 


99734 


994 


99739 


99743 


99747 


99752 


99756 


99760 


99765 


99769 


99774 


99778 


995 


99782 


99787 


99791 


99795 


99800 


99804 


99808 


99813 


9981" 


99822 


996 


99826 


99830 


99835 


99839 


99843 


99848 


99852 


99856 


99861 


99865 


997 


99870 


99874 


99878 


99883 


99887 


99891 


99896 


99900 


99904 


99909 


998 


99913 


99917 


99922 


99926 


99930 


99935 


99939 


99944 


99948 


99952 


999 


99957 


99961 


1 99965 


99970 


99974 


» 99978 


99983 


99987 


99991 


99996 



106 Artificial Sines, Tang, and Sec. Degree. 



M. 



Sine. 
Inf. Neg. 


Co-sine. 
~10 ^00000 


Tangent. 


Co-tang. 


Secant. 


Co-secant 





Inf. Neg. 


Infinite. 


"ioTooooo 


Infinite. 


60 


1 


6.46373 


10.00000 


6.46373 


13.53627 


10.00000 


13.53627 


59 


2 


76476 


00000 


76476 


23524 


00000 


23524 


58 


3 


94085 


00000 


94085 


05915 


00000 


05915 


57 


4 


7.06579 


00000 


7.06579 


12.93421 


00000 


12.93421 


56 


5 


16270 


00000 


16270 


83730 


00000 


83730 


55 


6 


24188 


00000 


24188 


75812 


00000 


75812 


54 


7 


30882 


00000 


30882 


69118 


00000 


69118 


53 


8 


36682 


00000 


36682 


63318 


00000 


63318 


52 


9 


41797 


00000 


41797 


58203 


00000 


58203 


51 


10 


46373 


00000 


46373 


53627 


00000 


53627 


50 


11 


7.50512 


10.00000 


7.50512 


12.49488 


10.00000 


12.49438 4 


12 


54291 


00000 


54291 


45709 


00000 


45709 


48 


13 


57767 


00000 


57767 


42233 


00000 


42233 


47 


14 


60985 


00000 


60986 


39014 


00000 


39015 


46 


15 


63982 


00000 


63982 


36018 


00000 


36018 


45 


16 


66784 


00000 


66785 


33215 


00000 


33216 


44 


17 


69417 


9.99999 


69418 


30582 


00001 


30583 


43 


18 


71900 


99999 


71900 


28100 


00001 


28100 


42 


19 


74248 


99999 


74248 


25752 


00001 


25752 


41 


20 


76475 


99999 


76476 


23524 


00001 


23525 


40 


21 


7.78594 


9.99999 


7.78595 


12.21405 


10.00001 


12.21406 


39 


22 


80615 


99999 


80615 


19385 


00001 


19385 


38 


23 


82545 


99999 


82546 


17454 


00001 


17455 


37 


24 


84393 


99999 


84394 


15606 


00001 


15607 


36 


25 


86166 


99999 


86167 


13833 


00001 


13834 


35 


26 


87870 


99999 


87871 


12129 


00001 


12130 


34 


27 


89509 


99999 


89510 


10490 


00001 


10491 


33 


28 


91088 


99999 


91089 


08911 


00001 


08912 


32 


29 


92612 


99998 


92613 


07387 


00002 


07388 


31 


30 


94084 


99998 


94086 


05914 


00002 
10.00002 


05910 
12.04492 


30 

29 


31 


7.95508 


9.99998 


7.95510 


12.04490 


32 


96887 


99998 


96889 


03111 


00002 


03113 


28 


33 


98223 


99998 


98225 


01775 


00002 


01777 


27 


34 


99520 


99998 


99522 


00478 


00002 


00480 


26 


35 


8.00779 


99998 


8.00781 


11.99219 


00002 


11.99221 


25 


36 


02002 


99998 


02004 


97996 


00002 


97998 


24 


37 


03192 


99997 


03194 


96806 


00003 


96808 


23 


38 


04350 


99997 


04353 


95647 


00003 


95650 


22 


39 


05478 


99997 


05481 


94519 


00003 


94522 


21 


40 


06578 


99997 
9-99997 


06581 
8.07653 


93419 


00003 


93422 


20 
19 


41 


8.07650 


11.92347 


10.00003 


11.92350 


42 


08696 


99997 


03700 


91300 


00003 


91304 


18 


43 


09718 


99997 


09722 


90278 


00003 


90282 


17 


44 


10717 


99996 


10720 


89280 


00004 


89283 


16 


45 


11693 


99996 


11696 


88304 


00004 


88307 


15 


46 


12647 


99996 


12651 


87349 


00004 


87353 


14 


47 


13581 


99996 


13585 


86415 


00004 


86419 


13 


48 


14495 


99996 


14500 


85500 


00004 


85505 


12 


49 


15391 


99996 


15395 


84605 


00004 


84609 


11 


50 


16268 


99995 


16273 
~~ 8. 17133 


83727 


00005 
"To. 00005 


83732 
11.82872 


10 
9 


51 


8.17128 


9.99995 


11.82867 


52 


17971 


99995 


17976 


82024 


00005 


82029 


8 


53 


18798 


99995 


18804 


81196 


00005 


81202 


7 


54 


19610 


99995 


19616 


80384 


00005 


80390 


6 


55 


20407 


99994 


20413 


79587 


00006 


79593 


5 


56 


21189 


99994 


21195 


78805 


00006 


78811 


4 


57 


21958 


99994 


21964 


78036 


00006 


78042 


3 


58 


22713 


99994 


22720 


77280 


00006 


77287 


2 


59 


23456 


99994 


23462 


76538 


00006 


76544 


1 


60 


24186 


99993 


24192 


75808 


00007 
Co-secant 


75814 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Secant. 


M. 



89 Degrees. 



Artificial Sines, Tang, and Sec. 1 Degree. 109 



VI. 



Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 




8.24186 


9.99993 


8.24192 


11.75808 


10.00007 


11.75814 


60 


1 


24903 


99993 


24910 


75090 


00007 


75097 


59 


2 


25609 


99993 


25616 


74384 


00007 


74391 


58 


3 


26304 


99993 


26312 


73688 


00007 


73696 


57 


■ 4 


26988 


99992 


26996 


73004 


00008 


73012 


56 


5 


27661 


99992 


27669 


72331 


00008 


72339 


55 


6 


28324 


99992 


28332 


71668 


00008 


71676 


54 


7 


28977 


99992 


28986 


71014 


00008 


71023 


53 


8 


29621 


99992 


29629 


70371 


00008 


70379 


52 


9 
10 


30255 


99991 


30263 


69737 


00009 


69745 


51 


{.30879 


9.99991 


8.30888 


11.69112 


10.00009 


11.69121 


50 


11 


31495 


99991 


31505 


68495 


00009 


68505 


49 


, 12 


32103 


99990 


32112 


67888 


00010 


67897 


48 


13 


32702 


99990 


32711 


67289 


00010 


67298 


47 


14 


33292 


99990 


33302 


66698 


00010 


66708 


46 


15 


33875 


99990 


33886 


66114 


00010 


66125 


45 


16 


34450 


99989 


34461 


65539 


00011 


65550 


44 


17 


35018 


99989 


35029 


64971 


00011 


64982 


43 


18 


35578 


99989 


35590 


64410 


00011 


64422 


42 


19 


36131 


99989 


36143 


63857 


00011 


63869 


41 


20 


8.36678 


9.99988 


8.36689 


11.63311 


10.00012 


11.63322 


40 


21 


37217 


99988 


37229 


62771 


00012 


62783 


39 


22 


37750 


99988 


37762 


62238 


00012 


62250 


38 


• 23 


38276 


99987 


38289 


61711 


00013 


61724 


37 


24 


38796 


99987 


38809 


61191 


00013 


61204 


36 


25 


39310 


99987 


39323 


60677 


00013 


60690 


35 


26 


39818 


99986 


39832 


60168 


00014 


60182 


34 


27 


40320 


99986 


40334 


59666 


00014 


59680 


33 


28 


40816 


99986 


40830 


59170 


00014 


59184 


32 


, 29 


41307 


99985 
9.99985 


41321 


58679 


00015 


58693 


31 


30 


8.41792 


8.41807 


11.58193 


10.00015 


11.58208 


30 


31 


42272 


99985 


42287 


57713 


00015 


57728 


29 


32 


42746 


99984 


42762 


57238 


00016 


57254 


28 


33 


43216 


99984 


43232 


56768 


00016 


56784 


27 


34 


43680 


99984 


43696 


56304 


00016 


56320 


26 


35 


44139 


99983 


44156 


55844 


00017 


55861 


25 


36 


44594 


99983 


44611 


55389 


00017 


55406 


24 


37 


45044 


99983 


45061 


54939 


00017 


54956 


23 

22 


38 


45489 


99982 


45507 


54493 


00018 


54511 


39 


45930 


99982 


45948 


54052 


00018 


54070 


21 


40 


8.46366 


9.99982 


8.46385 


11.53615 


10.00018 


11.53634 


20 


41 


46799 


99981 


46817 


53183 


00019 


53201 


19 


42 


47226 


99981 


47245 


52755 


00019 


52774 


18 


43 


47650 


99981 


47669 


52331 


00019 


52350 


17 


44 


48069 


99980 


48089 


51911 


00020 


51931 


16 


45 


48485 


99980 


48505 


51495 


00030 


51515 


15 


46 


48896 


99979 


48917 


51083 


00021 


51104 


14 


47 


49304 


99979 


49325 


50675 


00021 


50696 


13 


48 


49708 


99979 


49729 


50271 


00021 


50292 


12 


49 


50108 


99978 


50130 


49870 


00022 


49892 


11 


50 


8.50504 


9.99978 


8.50527 


11.49473 


10.00022 


11.49496 


10 


51 


50897 


99977 


50920 


49080 


00023 


49103 


9 


52 


51287 


99977 


51310 


48690 


00023 


48713 


8 


53 


51673 


99977 


51696 


48304 


00023 


48327 


7 


54 


52055 


99976 


52079 


47921 


00024 


47945 


6 


55 


52434 


99976 


52459 


47541 


00024 


47566 


5 


56 


52810 


99975 


52835 


47165 


00025 


47190 


4 


57 


53183 


99975* 


53208 


46792 


00025 


46817 


3 


, 58 


53552 


99974 


53578 


46422 


00026 


46448 


2 


59 


53919 


99974 


53945 


46055 


00026 


46081 


1 


60 


54282 


99974 


54308 


45692 


00026 


45718 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 



33* 



88 Decrees. 



f 10 



Artificial Sines, Tang, and Sec. 2 Degrees. 



AJ. 


Sine. 


Co-sine. 


Tangent. 
8.54308 


Co-tang. 
11.45692 


Secant. 
10.00026 " 


Jo-secant 1 
11.45718 " 


60 





8.54282 


9.99974 


1 


54642 


99973 


54669 


45331 


00027 


45358 


59 


2 


54999 


99973 


55027 


44973 


00027 


45001 


58 


3 


55354 


99972 


55382 


44618 


00028 


44646 


57 


4 


55705 


99972 


55734 


44266 


00023 


44295 


56 


5 


56054 


99971 


56083 


43917 


00029 


43946 


55 


6 


56400 


99971 


56429 


43571 


00029 


43600 


54 


7 


56743 


99970 


56773 


43227 


00030 


43257 


53 


8 


57084 


99970 


57114 


42886 


00030 


42916 


52 


3 io 


57421 

8.57757 


99969 


57452 


42548 


00031 


42579 


51 

50" 


9.99969 


8.57788 


11.42212 


10.00031 


11.42243 


ii 


58089 


99968 


58121 


41379 


00032 


41911 


49 


12 


58419 


99968 


58451 


41549 


00032 


41581 


48 


13 


58747 


99967 


58779 


41221 


00033 


41253 


47 


14 


59072 


99967 


59105 


40895 


00033 


40928 


46 


15 


59395 


99967 


59428 


40572 


00033 


40605 


45 


16 


59715 


99966 


59749 


40251 


00034 


40285 


44 


17 


60033 


99966 


60068 


39932 


50034 


39967 


43 


18 


60349 


99965 


60384 


39616 


90035 


39651 


42 


19 


60662 


99964 


60698 


39302 


30036 
10.00036 


39338 


41 


20 


8.60973 


9.99964 


8.61009 


11.38991 


11.39027 


~40" 


21 


61282 


99963 


61319 


38681 


00037 


38718 


39 


22 


61589 


99963 


61626 


38374 


00037 


38411 


38 


23 


61894 


99962 


61931 


38069 


00038 


38106 


37 


24 


62196 


99962 


62234 


37766 


00038 


37804 


36 


25 


62497 


99961 


62535 


37465 


00039 


37503 


35 


26 


62795 


99961 


62834 


37166 


00039 


37205 


34 


27 


63091 


99960 


63131 


36869 


00040 


36909 


33 


23 


63385 


99960 


63426 


36574 


00040 


36615 


32 


29 
"~30~ 


63678 
8.63968 


99959 
9.99959 


63713 
8.64009 


36282 


00041 


36322 


31 


11.35991 


10.00041 


11.36032 


30 


31 


64256 


99958 


64298 


35702 


00042 


35744 


29 


32 


64543 


99958 


64585 


35415 


00042 


35457 


28 


33 


64827 


99957 


64870 


35130 


00043 


35173 


27 


34 


65110 


99956 


65154 


34846 


00044 


34890 


26 


35 


65391 


99956 


65435 


34565 


00044 


34609 


25 


36 


65670 


99955 


65715 


34285 


00045 


34330 


24 


37 


65947 


99955 


65993 


34007 


00045 


34053 


23 


38 


66223 


99954 


66269 


33731 


00046 


33777 


22 


39 


66497 


99954 


66543 


33457 


00046 


33503 


21 
20 


40 


8.66769 


9.99953 


8.66816 


11.33184 


10.00047 


11.33231 


41 


i 67039 


99952 


67087 


32913 


00048 


32961 


19 


42 


67308 


99952 


67356 


32644 


00048 


32692 


18 


43 


67575 


99951 


67624 


32376 


00049 


32425 


17 


44 


67841 


99951 


67890 


32110 


00049 


32159 


16 


45 


68104 


99950 


68154 


31846 


00050 


31896 


15 


46 


I 68367 


99949 


68417 


31583 


00051 


31633 


14 


47 


68627 


99949 


68678 


31322 


00051 


31373 


13 


43 


63886 


99948 


68938 


31062 


00052 


31114 


12 


49 


69144 


99948 


69196 


30804 


00052 


30856 


11 


50 


8.69400 


9.99947 


8.69453 


11.30547 


10.00053 


11.30600 


10 


51 


69654 


99946 


69708 


30292 


00054 


30346 


9 


52 


69907 


99946 


69962 


30038 


00054 


30093 


8 


53 


70159 


99945 


70214 


29786 


00055 


29841 


7 


54 


70409 


99944 


70465 


29535 


00056 


29591 


6 


55 


70658 


99944 


70714 


29286 


00056 


29342 


5 


56 


70905 


99943 


70962 


29038 


00057 


29095 


4 


57 


71151 


99942 


71208 


28792 


00058 


28849 


3 


58 


71395 


99942 


71453 


28547 


00058 


28605 


2 


59 


71638 


99941 


71697 


28303 


00059 


28362 


1 


60 


71880 


99940 


71940 


28060 


00060 


28120 







Co-sine. 


Sine. 


Co-tan°:. 


Tangent. 


Co-secpnt 


Secant. 


M. 



87 D( 



Artificial Sines, Tans;, and Sec. 3 Degrees. 1 1 1 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tanic. 


Secant. 


Co-secaut | 





8.71880 


9.99940 


8.71940 


11.28060 


10.00060 


11.281-u! 60 


1 


72120 


99940 


72181 


27819 


00060 


27880 


59 


2 


72359 


99939 


72420 


27580 


00061 


27641 


51j 


3 


72597 


99938 


72659 


27341 


00062 


27403 


57 


4 


72834 


99938 


72396 


27104 


00062 


27166 


56 


5 


73069 


99937 


73132 


26868 


00063 


26931 


55 


6 


73303 


99936 


73366 


26634 


00064 


26697 


54 


7 


73535 


99936 


73600 


26400 


00064 


26465 


53 


8 


73767 


99935 


73832 


26168 


00065 


26233 


52 


9 


73997 


99934 


74063 


25937 


00066 


26003 


51 

~50" 


10 


8.74226 


9.99934 


8.74292 


1 : .25708 


10.00066 


11.25774 


11 


74454 


99933 


74521 


25479 


00067 


25546 


49 


12 


74680 


99932 


74748 


25252 


00068 


25320 


48 


13 


74906 


99932 


74974 


25026 


00068 


25094 


47 


14 


75130 


99931 


75199 


24801 


00069 


24870 


46 


15 


75353 


99930 


75423 


24577 


00070 


24647 


45 


16 


75575 


99929 


75645 


24355 


00071 


24425 


44 I 


17 


75795 


99929 


75867 


24133 


00071 


24205 


43 


18 


76015 


99928 


76087 


23913 


00072 


23985 


42 


19 


76234 


99927 


76306 


23694 


00073 


23766 


41 
40' 


20 


8.76451 


9.99926 


8.76525 


11.23475 


10.00074 


11.23549 


21 


76667 


99926 


76742 


23258 


00074 


23333 


39 


22 


76883 


99925 


76958 


23042 


00075 


23117 


38 


23 


77097 


99924 


77173 


22827 


00076 


22903 


37 


24 


77310 


99923 


77387 


22613 


00077 


22690 


36 


25 
26 
27 


77522 


99923 


77600 


22400 


00077 


22478 


35 


77733 


99922 


77811 


22189 


00078 


22267 


34 


77943 


99921 


78022 


21978 


00079 


22057 


33 


! 28 


78152 


99920 


78232 


21768 


00080 


21848 


32 


29. 


78360 


99920 


78441 


21559 


00080 


21640 


31 


30 


8.78568 


9.99919 


8.78649 


11.21351 


10.00081 


11.21432 


30 


31 


78774 


99918 


78855 


21145 


00082 


21226 


29 


32 


78979 


99917 


79061 


20939 


00083 


21021 


28 


33 


79183 


99917 


79266 


20734 


00083 


20817 


27 


34 


79386 


99916 


79470 


20530 


00084 


20614 


26 


35 


79588 


99915 


79673 


20327 


00085 


20412 


25 


36 


79789 


99914 


79875 


20125 


00086 


20211 


24 


37 


79990 


99913 


80076 


19924 


00087 


20010 


23 


38 


80189 


99913 


80277 


19723 


00087 


19811 


22 


39 


80388 


99912 


80476 


19524 


00088 


19612 


21 
"20" 


40 


8.80585 


9.99911 


8.80674 


11.19326 


10.00089 


11.19415 


41 


80782 


99910 


80872 


19128 


00090 


19218 


19 


42 


80978 


99909 


81068 


18932 


00091 


19022 


18 


. 43 


81173 


99909 


81264 


18736 


00091 


18827 


17 


44 


81367 


99908 


81459 


18541 


00092 


18633 


16 


45 


81560 


99907 


81653 


18347 


00093 


18440 


15 


46 


81752 


99906 


81846 


18154 


00094 


18248 


14 


47 


81944 


99905 


82038 


17962 


00095 


18056 


13 


48 


82134 


99904 


82230 


17770 


00096 


17866 


12 


49 
50 


82324 
8.82513 


99904 


82420 


17580 


00096 


17676 


11 

10 


9.99903 


8.82610 


11.17390 


10.00097 


11.17487 


51 


82701 


99902 


82799 


17201 


00098 


17299 


9 


i 52 


82888 


99901 


82987 


17013 


00099 


17112 


8 


53 


83075 


99900 


83175 


16825 


00100 


16925 


7 


54 


83261 


99899 


83361 


16639 


00101 


16739 


6 


55 


83446 


99898 


83547 


16453 


00102 


16554 


5 


56 


83630 


99898 


83732 


16268 


00102 


16370 


4 


57 


83813 


99897 


83916 


16084 


00103 


16187 


3 


58 


83996 


99896 


84100 


15900 


00104 


16004 


2 


59 


84177 


99895 


84282 


15718 


00105 


15823 


1 


60 


84358 


99894 


84464 


15536 


00106 


15642 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 



86 Degrees. 



112 Artificial Sines, Tang, and Sec. 4 Degrees. 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 
11.15642 


60 







8.84353 


9.99894 


8.84464 


11.15536 


10.00106 




1 


84539 


99893 


84646 


15354 


00107 


15461 


59 




2 


84718 


99392 


84826 


15174 


00108 


15282 


58 




3 


84897 


99891 


85006 


14994 


00109 


15103 


57 




4 


85075 


99391 


85185 


14815 


00109 


14925 


56 




5 


85252 


99890 


85363 


14637 


00110 


14743 


55 




6 


85429 


99889 


85540 


14460 


00111 


14571 


54 




7 


85605 


99888 


85717 


14283 


00112 


14395 


53 




8 


85780 


99887 


85893 


14107 


00113 


14220 


52 




9 


85955 


99886 


86069 


13931 


00114 


14045 


J] 




10 


8.86128 


9.99885 


8.86243 


11.13757 


10.00115 


11.13872 


50 i 


11 


86301 


99884 


86417 


13583 


00116 


13699 


49 




12 


86474 


99883 


86591 


13409 


00117 


13526 


48 




13 


86645 


99882 


86763 


13237 


00118 


13355 


47 




14 


86816 


99881 


86935 


13065 


00119 


13184 


46 




15 


86987 


99880 


87106 


12894 


00120 


13013 


45 




16 


87156 


99879 


87277 


12723 


00121 


12844 


44 




17 


87325 


99879 


87447 


12553 


00121 


12675 


43 




18 


87494 


99378 


87616 


12384 


00122 


12506 


42 




19 


87661 


99877 


87785 


12215 


00123 


12339 
11.12171 


41 
40 




20 


8.87829 


9.99876 


8.87953 


11.12047 


10.00124 




21 


87995 


99875 


88120 


11880 


00125 


12005 


39 




22 


88161 


99874 


88287 


11713 


00126 


11839 


38 




23 


88326 


99873 


88453 


11547 


00127 


11674 


37 




24 


88490 


99872 


88618 


11382 


00128 


11510 


36 




25 


88654 


99871 


88783 


11217 


00129 


11346 


35 




26 


88817 


99870 


88943 


11052 


00130 


11183 


34 




27 


88980 


99869 


89111 


10889 


00131 


11020 


33 




28 


89142 


99868 


89274 


10726 


00132 


10858 


32 




29 


89304 


99867 


89437 


10563 


00133 


10696 


31 
30 




30 


8.89464 


9.99866 


8.89598 


11.10402 


10.00134 


11.10536 




31 


89625 


99865 


89760 


10240 


00135 


10375 


29 




32 


89784 


99864 


89920 


10080 


00136 


10216 


28 




33 


89943 


99863 


90080 


09920 


00137 


10057 


27 




34 


90102 


99862 


90240 


09760 


00138 


09898 


26 




35 


90260 


99861 


90399 


09601 


00139 


09740 


25 




36 


90417 


99860 


90557 


09443 


00140 


09533 


24 




37 


90574 


99859 


90715 


09285 


00141 


09426 


23 




38 


90730 


99858 


90872 


09123 


00142 


09270 


22 




39 


90885 


99857 


91029 


08971 


00143 


09115 


21 




40 


8.91040 


9.99856 


8.91185 


11.08815 


10.00144 


11.08960 


20 




41 


91195 


99855 


91340 


08660 


00145 


08805 


19 




42 


91349 


99854 


91495 


08505 


00146 


08651 


18 




43 


91502 


99853 


91650 


08350 


00147 


08498 


17 




: 44 


91655 


99352 


91803 


08197 


00148 


08345 


16 




45 


91807 


99851 


9195" 


08043 


00149 


08193 


15 




46 


91959 


99850 


921 lu 


07890 


00150 


08041 


14 




47 


92110 


99848 


92262 


07738 


00152 


07890 


13 




48 


92261 


99847 


92414 


07586 


00153 


07739 


12 




49 


92411 


99846 


92565 


07435 


00154 


07589 


11 




50 


8.92561 


9.99845 


8.92716 


11.07284 


10.00155 


11.07439 


10 




51 


92710 


99344 


92866 


07134 


00156 


07290 


9 




52 


92859 


99843 


93016 


06984 


00157 


07141 


8 




53 


93007 


99842 


93165 


06835 


00158 


06993 


7 




54 


93154 


99841 


93313 


06687 


00159 


06846 


6 




55 


93301 


99840 


93462 


06538 


00160 


06699 


5 




56 


93448 


99839 


93609 


06391 


00161 


06552 


4 




57 


93594 


99838 


93756 


06244 


00162 


06406 


3 




58 


93740 


99837 


93903 


06097 


00163 


06260 2 




59 


93885 


99836 


94049 


05951 


00164 


06115 1 




60 


94030 


99834 


94195 


05805 


00166 


05970 






Co-sine. 


Sine. 


Co-tang. 


Tangent. | 


Co-secant 


Secant. 1 M. 





85 Degrees. 



Artificial Sines, Tang, and Sec. 5 Degrees. 113 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 
11.05970 


60 





8.94030 


9.99834 


8.94195 


11.05805 


10.00166 


1 


94174 


99833 


94340 


05660 


00167 


05826 


59 


2 


■ 94317 


99832 


94485 


05515 


00168 


05683 


58 


• 3 


94461 


99831 


94630 


05370 


00169 


05539 


57 


4 


94603 


99830 


94773 


05227 


00170 


05397 


56 


5 


94746 


99829 


94917 


05083 


00171 


05254 


55 


6 


94887 


99828 


95060 


04940 


00172 


05113 


54 


7 


95029 


99827 


95202 


04798 


00173 


04971 


53 


8 


95170 


99825 


95344 


04656 


00175 


04830 


52 


9 
10 


95310 
8.95450 


99824 


95486 


04514 


00176 
10.00177 


04690 


51 


9.99823 


8.95627 


11.04373 


11.04550 


50 


11 


95589 


99822 


95767 


04233 


00178 


04411 


49 


12 


95728 


99821 


95908 


04092 


00179 


04272 


48 


13 


95867 


99820 


96047 


03953 


00180 


04133 


47 


14 


96005 


99819 


96187 


03813 


00181 


03995 


46 


15 


96143 


99817 


96325 


03675 


00183 


03857 


45 


16 


96280 


99816 


96464 


03536 


00184 


03720 


44 


17 


96417 


99815 


96602 


03398 


00185 


03583 


43 


18 


96553 


99814 


96739 


03261 


00186 


03447 


42 


19 


96689 


99813 


96877 


03123 


00187 


03311 


41 
40 


20 


8.96825 


9.99812 


8.97013 


11.02987 


10.00188 


11.03175 


21 


96960 


99810 


97150 


02850 


00190 


03040 


39 


22 


97095 


99809 


97285 


02715 


00191 


02905 


38 


23 


97229 


99808 


97421 


02579 


00192 


02771 


37 


24 


97363 


99807 


97556 


02444 


00193 


02637 


36 


25 


97496 


99806 


97691 


02309 


00194 


02504 


35 


26 


97629 


99804 


97825 


02175 


00196 


02371 


34 


27 


97762 


99803 


97959 


02041 


00197 


02238 


33 


28 


97894 


99802 


98092 


01908 


00198 


02106 


32 


29 


98026 


99801 


98225 


01775 
11.01642 


00199 


01974 


31 
30 


30 


8.98157 


9.99800 


8.98358 


10.00200 


11.01843 


31 


98288 


99798 


98490 


01510 


00202 


01712 


29 


32 


98419 


99797 


98622 


01378 


00203 


01581 


28 


33 


98549 


99796 


98753 


01247 


00204 


01451 


27 


34 


98679 


99795 


98884 


01116 


00205 


01321 


26 


35 


98808 


99793 


99015 


00985 


00207 


01192 


25 


36 


98937 


99792 


99145 


00855 


00208 


01063 


24 


37 


99066 


99791 


99275 


00725 


00209 


00934 


23 


38 


99194 


99790 


99405 


00595 


00210 


00806 


22 


39 


99322 


99788 


99534 


00466 


00212 


00678 


21 


40 


8.99450 


9.99787 


8.99662 


11.00338 


10.00213 


11.00550 


20 


41 


99577 


99786 


99791 


00209 


00214 


00423 


19 


42 


99704 


99785 


99919 


00081 


00215 


00296 


18 


43 


99830 


99783 


9.00046 


10.99954 


00217 


00170 


17 


44 


99956 


99782 


00174 


99826 


00218 


00044 


16 


45 


9.00082 


99781 


00301 


99699 


00219 


10.99918 


15 


46 


00207 


99780 


00427 


99573 


00220 


99793 


14 


47 


00332 


99778 


00553 


99447 


00222 


99668 


13 


48 


00456 


99777 


00679 


99321 


00223 


99544 


12 


49 


00581 


99776 


00805 


99195 


00224 


99419 


11 


. 50 


9.00704 


9.99775 


9.00930 


10.99070 


10.00225 


10.99296 


10 


' 51 


00828 


99773 


01055 


98945 


00227 


99172 


9 


52 


00951 


99772 


01179 


98821 


00228 


99049 


8 


53 


01074 


99771 


01303 


98697 


00229 


98926 


7 


54 


01196 


99769 


91427 


98573 


00231 


98804 


6 


55 


013 6 


99768 


01550 


98450 


00232 


98682 


5 


56 


01440 


99767 


01673 


98327 


00233 


98560 


4 


57 


01561 


99765 


01796 


98204 


00235 


98439 


3 


58 


01682 


99764 


01918 


98082 


00236 


98318 


2 


59 


01803 


99763 


02040 


97960 


00237 


98197 


1 


60 


01923 


99761 


02162 


97838 


00239 


98077 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 



84 Degrees. 3 L> 



114 Artificial Sines, Tang, and Sec. 6 Degrees 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 
10.98077 


60 





9.01923 


9.99761 


9.02162 


10.97838 


10.00239 


1 


02043 


99760 


02283 


97717 


00240 


97957 


59 


2 


02163 


99759 


02404 


97596 


00241 


97837 


58 


3 


02283 


99757 


02525 


97475 


00243 


97717 


57 


4 


02402 


99756 


02645 


97355 


00244 


97598 


56 


5 


02520 


99755 


02766 


97234 


00245 


97480 


55 


6 


02639 


99753 


02885 


97115 


00247 


97361 


54 


7 


02757 


99752 


03005 


96995 


00248 


97243 


53 


8 


02874 


99751 


03124 


96876 


00249 


97126 


52 


9 


02992 


99749 


03242 


96758 


00251 


97008 


51 


! io 


9.03109 


9.99748 


9.03361 


10.96639 


10.00252 


10.96891 


50 


11 


03226 


99747 


03479 


96521 


00253 


96774 


49 


12 


03342 


99745 


03597 


96403 


,00255 


96658 


48 


13 


03458 


99744 


03714 


96286 


00256 


96542 


47 


14 


03574 


99742 


03832 


96168 


00258 


96426 


46 


15 


03690 


99741 


03948 


96052 


00259 


96310 


45 


16 


03805 


99740 


04065 


95935 


00260 


96195 


44 


17 


03920 


99738 


04181 


95819 


00262 


96080 


43 


18 


04034 


99737 


04297 


95703 


00263 


95966 


42 


19 


04149 


99736 


04413 


95587 


00264 


95851 


41 
40 


20 


9.04262 


9.99734 


9.04528 


10.95472 


10.00266 


10.95738 


21 


04376 


99733 


04643 


95357 


00267 


95624 


39 


22 


04490 


99731 


04753 


95242 


00269 


95510 


38 


23 


04603 


99730 


04873 


95127 


00270 


95397 


37 


24 


04715 


99728 


04987 


95013 


00272 


95285 


36 


25 


04828 


99727 


05101 


94899 


00273 


95172 


35 


26 


04940 


99726 


05214 


94786 


00274 


95060 


34 


27 


05052 


99724 


05323 


94672 


00276 


94948 


33 


28 


05164 


99723 


05441 


94559 


00277 


94836 


32 


29 


05275 


99721 


05553 


94447 


00279 


94725 


31 


30 


9.05386 


9.99720 


9.05666 


10.94334 


TO. 00280 


10.94614 


30 


31 


05497 


99718 


05778 


94222 


00282 


94503 


29 


32 


05607 


99717 


05890 


94110 


00283 


94393 


23 


33 


05717 


99716 


06002 


93998 


00284 


94283 


27 


34 


05827 


99714 


06113 


93887 


00286 


94173 


26 


35 


05937 


99713 


06224 


93776 


00287 


94063 


25 


36 


06046 


99711 


06335 


93665 


00289 


93954 


24 


37 


06155 


99710 


06445 


93555 


00290 


93845 


23 


38 


06264 


99708 


06556 


93444 


00292 


93736 


22 


39 


06372 


99707 


06666 
9.06775 


93334 


00293 
10.00295 


93628 


21 


40 


9.06481 


9.99705 


10.93225 


10.93519 


20 


41 


06589 


99704 


06885 


93115 


00296 


93411 


19 


42 


06696 


99702 


06994 


93006 


00298 


93304 


18 


43 


06804 


99701 


07103 


92897 


00299 


93196 


17 


44 


06911 


99699 


07211 


92789 


00301 


93089 


16 


: 45 


07018 


99698 


07320 


92680 


00302 


92982 


15 


46 


07124 


99696 


07423 


92572 


00304 


92876 


14 


47 


07231 


99695 


07536 


92464 


00305 


92769 


13 


48 


07337 


99693 


07643 


92357 


00307 


92663 


12 


49 


07442 


99692 


07751 


92249 


00308 


92558 


11 


50 


9.07548 


9.99690 


9.07858 


10.92142 


10.00310 


10.92452 


~W 


51 


07653 


99689 


07964 


92036 


00311 


92347 


9 


52 


07758 


99687 


08071 


91929 


00313 


92242 


8 


53 


07863 


99686 


08177 


91823 


00314 


92137 


7 


54 


07968 


99684 


08283 


91717 


00316 


92032 


6 


55 


08072 


99683 


08389 


91611 


00317 


91928 


5 


56 


08176 


99681 


08495 


91505 


00319 


91824 


4 


57 


08230 


99680 


08600 


91400 


00320 


91720 


3 


58 


08383 


99678 


08705 


91295 


00322 


91617 


2 


59 


08486 


99677 


08810 


91190 


00323 


91514 


1 


60 


08589 


99675 


08914 


91086 


00325 


91411 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


mT| 



83 Decrees 



Artificial Sines, Tang, and Sec. 7 Degrees. 115 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 







9.08589 


9.99675 


9.08914 


10.91086 


10.00325 


10-91411 


60 ' 


1 


08692 


99674 


09019 


90981 


00326 


91308 


59 


2 


08795 


99672 


09123 


90877 


00328 


91205 


58 


3 


08897 


99670 


09227 


90773 


00330 


91103 


57 


4 


08999 


99669 


09330 


90670 


00331 


91001 


56 


5 


09101 


99667 


09434 


90566 


00333 


90899 


55 


6 


09202 


99666 


09537 


90463 


00334 


90798 


54 


7 


09304 


99664 


09640 


90360 


00336 


90696 


53 


8 


09405 


99663 


09742 


90258 


00337 


90595 


52 


9 


09506 


99661 
9.99659 


09845 
9.09947 


90155 


00339 


90494 


51 


10 


9.09606 


10.90053 


10.00341 


10.90394 


50 


11 


09707 


99658 


10049 


89951 


00342 


90293 


49 


12 


09807 


99656 


10150 


89850 


00344 


90193 


48 


13 


09907 


99655 


10252 


89748 


00345 


90093 


47 


14 


10006 


99653 


10353 


89647 


00347 


89994 


46 


15 


10106 


99651 


10454 


89546 


00349 


89894 


45 


16 


10205 


99650 


10555 


89445 


00350 


89795 


44 


17 


10304 


99648 


10656 


89344 


00352 


89696 


43 


18 


10402 


99647 


10756 


89244 


00353 


89598 


42 


19 


10501 


99645 


10856 


89144 


00355 


89499 


41 : 

40 


20 


9.10599 


9.99643 


9.10956 


10.89044 


10.00357 


10.89401 


21 


10697 


99642 


11056 


88944 


00358 


89303 


39 i 


22 


10795 


99640 


11155 


88845 


00360 


89205 


38 


23 


10893 


99638 


11254 


88746 


00362 


89107 


37 


24 


10990 


99637 


11353 


88647 


00363 


89010 


36 


25 


11087 


99635 


11452 


88548 


00365 


88913 


35 


26 


11184 


99633 


11551 


88449 


00367 


88816 


34 l 


27 


11281 


99632 


11649 


88351 


00368 


88719 


33 


28 


11377 


99630 


11747 


88253 


00370 


88623 


32 


29 


11474 


99629 


11845 


88155 


00371 


88526 


31 


30 


9.11570 


9.99627 


9.11943 


10.88057 


10.00373 


10.88430 


30 


31 


11666 


99625 


12040 


87960 


00375 


88334 


29 


32 


11761 


99624 


12138 


87862 


00376 


88239 


28 


33 


11857 


99622 


12235 


87765 


00378 


88143 


27 


34 


11952 


99620 


12332 


87668 


00380 


88048 


26 


35 


12047 


99618 


12428 


87572 


00382 


87953 


25 


36 


12142 


99617 


12525 


87475 


00383 


87858 


24 


37 


12236 


99615 


12621 


87379 


00385 


87764 


23 


38 


12331 


99613 


12717 


87283 


00387 


87669 


22 


39 


12425 


99612 


12813 


87187 


00388 
10.00390 


87575 


21 


40 


9.12519 


9.99610 


9.12909 


10.87091 


10.87481 


20 ' 


41 


12612 


99608 


13004 


86996 


00392 


87388 


19 


42 


12706 


99607 


13099 


86901 


00393 


87294 


18 


43 


12799 


99605 


13194 


86806 


00395 


87201 


17 


44 


12892 


99603 


13289 


86711 


00397 


87108 


16 


45 


12985 


99601 


13384 


86616 


00399 


87015 


15 


46 


13078 


99600 


13478 


86522 


00400 


86922 


14 


47 


13171 


99598 


13573 


86427 


00402 


86829 


13 


48 


13263 


99596 


13667 


86333 


00404 


86737 


12 


49 
50 


13355 
9.13447 


99595 


13761 


86239 


00405 
10.00407 


86645 
10.86553 


11 
10 


9.99593 


9.13854 


10.86146 


51 


13539 


99591 


13948 


86052 


00409 


86461 


9 


52 


13630 


99589 


14041 


85959 


00411 


86370 


8 


53 


13722 


99588 


14134 


85866 


00412 


86278 


7 


54 


13813 


99586 


14227 


85773 


00414 


86187 


6 


55 


13904 


99584 


14320 


85680 


00416 


86096 


5 


56 


13994 


99582 


14412 


85588 


00418 


86006 


4 


57 


14085 


99581 


14504 


85496 


00419 


85915 


3 


58 


14175 


99579 


14597 


85403 


00421 


85825 


2 


59 


14266 


99577 


14688 


85312 


00423 


85734 


1 


60 


14356 


99575 


14780 


85220 


00425 


85644 







Co-sinc. 


Sine. 


Co- tang. 


Tangent. 


Co-secant 


Secant. 


M. 



82 Degrees 



116 Artificial Sines, Tang, and Sec. 8 Degrees. 



M. 


Sine. 


Co-sine. 
9.99575 


Tangent. 
9.14780 


Co-tang. 
10.85220 


Secant. 
10.00425 


Co-secant 
10.85644 


60 





9.14356 


1 


14445 


99574 


14872 


85128 


00426 


85555 


59 


2 


14535 


99572 


14963 


85037 


00428 


85465 


58 


3 


14624 


99570 


15054 


84946 


00430 


85376 


57 


4 


14714 


99568 


15145 


84855 


00432 


85286 


56 


5 


14803 


99566 


15236 


84764 


00434 


85197 


5. r y 


6 


14891 


99565 


15327 


84673 


00435 


85109 


54 


7 


14980 


99563 


15417 


84583 


00437 


85020 


53 


8 


15069 


99561 


15508 


84492 


00439 


84931 


52 


9 


15157 


99559 


15598 
9.15688 


84402 


00441 


84843 
10.84755 


51 

To - 


10 


9.15245 


9.99557 


10.84312 


10.00443 


11 


15333 


99556 


15777 


84223 


00444 


84667 


49 


12 


15421 


99554 


15867 


84133 


00446 


84579 


48 


13 


15508 


99552 


15956 


84044 


00448 


84402 


47 


14 


15596 


99550 


16046 


83954 


00450 


84404 


46 


15 


15683 


99548 


16135 


83865 


00452 


84317 


45 


16 


15770 


99546 


16224 


83776 


00454 


84230 


44 


17 


15857 


99545 


16312 


83688 


00455 


84143 


43 


18 


15944 


99543 


16401 


83599 


00457 


84056 


42 


19 


16030 


99541 


16489 


83511 
10.83423 


00459 


83970 


41 


20 


9.16116 


9.99539 


9.16577 


10.00461 


10.83884 


40 


21 


16203 


99537 


16665 


83335 


00463 


83797 


39 


22 


16289 


99535 


16753 


83247 


00465 


83711 


38 


23 


16374 


99533 


16841 


83159 


00467 


83626 


37 j 


24 


16460 


99532 


16928 


83072 


00468 


83540 


36 ! 


25 


16545 


99530 


17016 


82984 


00470 


83455 


35 


26 


16631 


99528 


17103 


82897 


00472 


83369 


34 


27 


16716 


99526 


17190 


82810 


00474 


83284 


33 


28 


16801 


99524 


17277 


82723 


00476 


83199 


32 


29 


16886 


99522 


17363 


82637 


00478 


83114 


31 
30 


30 


9.16970 


9.99520 


9.17450 


10.82550 


10.00480 


10.83030 


31 


17055 


99518 


17536 


82464 


00482 


82945 


29 


32 


17139 


99517 


17622 


82378 


00483 


82861 


28 


33 


17223 


99515 


17708 


82292 


00485 


82777 


27 


34 


17307 


99513 


17794 


82206 


00487 


82693 


26 


35 


17391 


99511 


17880 


82120 


00489 


82609 


25 


36 


17474 


99509 


17965 


82035 


00491 


82526 


24 


37 


17558 


99507 


18051 


81949 


00493 


82442 


23 


38 


17641 


99505 


18136 


81864 


00495 


82359 


22 


39 


17724 


99503 


18221 


81779 


00497 


82276 
10.82193 


21 
~20~ 


40 


9.17807 


9.99501 


9.18306 


10.81b!?4 


10.00499 


41 


17890 


99499 


18391 


81609 


00501 


82110 


19 


42 


17973 


99497 


18475 


81525 


00503 


82027 


18 


43 


18055 


99495 


18560 


81440 


00505 


81945 


17 


44 


18137 


99494 


18644 


81356 


00506 


81863 


16 


45 


18220 


99492 


18728 


81272 


00508 


81780 


15 


46 


18302 


99490 


18812 


81188 


00510 


81698 


14 


47 


18383 


99488 


18896 


81104 


00512 


81617 


13 


48 


18465 


99486 


18979 


81021 


00514 


81535 


12 


49 


18547 


99484 


19063 


80937 
10.80854 


00516 


81453 


11 


50 


9.18628 


9.99482 


9.19146 


10.00518 


10.81372 


10 


51 


18709 


99480 


19229 


80771 


00520 


81291 


9 


52 


1»790 


99478 


19312 


80688 


00522 


81210 


8 


53 


18871 


99476 


19395 


80605 


00524 


81129 


7 


54 


18952 


99474 


19478 


80522 


00526 


81048 


6 


55 


19033 


99472 


19561 


80439 


00528 


80967 


5 


56 


19113 


99470 


19643 


80357 


00530 


80887 


4 


57 


19193 


99468 


19725 


80275 


00532 


80807 


3 


58 


19273 


99466 


19807 


80193 


>>0534 


80727 


2 


59 


19353 


99464 


19889 


80111 


00536 


80647 


1 1 


60 


19433 
Co-sine. 


99462 


19971 


80029 


00538 


80567 


-° 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


mJ 



81 Dfiiri 



Artificial Sines, Tang, and Sec. 9 Degrees. i i 7 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang;. 


Secant. 
10.00538 


Co-secant 







9.19433 


9.99462 


9.19971 


10.80029 


10.80567 


60 


1 


19513 


99460 


20053 


79947 


00540 


80487 


59 


2 


19592 


99458 


20134 


79866 


00542 


80408 


58 


3 


19672 


99456 


20216 


79784 


00544 


80328 


57 


4 


19751 


99454 


20297 


79703 


00546 


80249 


56 


5 


19830 


99452 


20378 


79622 


00548 


80170 


55 


6 


19909 


99450 


20459 


79541 


00550 


80091 


54 


7 


19988 


99448 


20540 


79460 


00552 


80012 


53 


8 


20067 


99446 


20621 


79379 


00554 


79933 


52 


9 


20145 


99444 
9.99442 


20701 
9.20782 


79299 


00556 


79855 


51 

~50f 


10 


9.20223 


10.79218 


10.00558 


10.79777 


11 


20302 


99440 


20862 


79138 


00560 


79698 


49 


12 


20380 


99438 


20942 


79058 


00562 


79620 


48 


13 


20458 


99436 


21022 


78978 


00564 


79542 


47 


14 


20535 


99434 


21102 


78898 


00566 


79465 


46 


15 


20613 


99432 


21182 


78818 


00568 


79387 


45 


16 


20691 


99429 


21261 


78739 


00571 


79309 


44 


17 


20768 


99427 


21341 


78659 


00573 


79232 


43 


18 


20845 


99425 


21420 


78580 


00575 


79155 


42 


19 


20922 


99423 


21499 


78501 


00577 


79078 


41 


20 


9.20999 


9.99421 


9.21578 


10.78422 


10.00579 


10.79001 


40 


21 


21076 


99419 


21657 


78343 


00581 


78924 


39 


22 


21153 


99417 


21736 


78264 


00583 


78847 


38 


23 


21229 


99415 


21814 


78186 


00585 


78771 


37 


24 


21306 


99413 


21893 


78107 


00587 


78694 


36 


25 


21382 


99411 


21971 


78029 


00589 


78618 


35 


26 


21458 


99409 


22049 


77951 


00591 


78542 


34 


27 


21534 


99407 


22127 


77873 


00593 


78466 


33 


28 


21610 


99404 


22205 


77795 


00596 


78390 


32 


29 


21685 


99402 


22283 


77717 


00598 


78315 


31 


30 


9.21761 


9-99400 


9.22361 


10.77639 


10.00600 


10.78239 


30 


31 


21836 


99398 


22438 


77562 


00602 


78164 


29 


32 


21912 


99396 


22516 


77484 


00604 


78088 


28 


33 


21987 


99394 


22593 


77407 


00606 


78013 


27 . 


34 


22062 


99392 


22670 


77330 


00608 


77938 


26 


35 


22137 


99390 


22747 


77253 


00610 


77863 


25 


36 


22211 


99388 


22824 


77176 


00612 


77789 


24 


37 


22286 


99385 


22901 


77099 


00615 


77714 


23 


38 


22361 


99383 


22977 


77023 


00617 


77639 


22 


39 


22435 


99381 


23054 


76946 


00619 


77565 
10.77491 


21 


40 


9.22509 


9.99379 


9.23130 


10.76870 


10.00621 


20 


41 


22583 


99377 


23206 


76794 


00623 


77417 


19 


42 


22657 


99375 


23283 


76717 


00625 


77343 


18 


43 


22731 


99372 


23359 


76641 


00628 


77269 


17 


44 


22805 


99370 


23435 


76565 


00630 


77195 


16 


45 


22878 


99368 


23510 


76490 


00632 


77122 


15 


46 


22952 


99366 


23586 


76414 


00634 


77048 


14 


47 


23025 


99364 


23661 


76339 


00636 


76975 


13 


48 


23098 


99362 


23737 


76263 


00638 


76902 


12 


49 


23171 


99359 


23812 


76188 


00641 


76829 


11 
10 


50 


9.23244 


9.99357 


9.23887 


10.76113 


10.00643 


10.76756 


51 


23317 


99355 


23962 


76038 


00645 


76683 


9 


52 


23390 


99353 


24037 


75963 


00647 


76610 


8 


53 


23462 


99351 


24112 


75888 


00649 


76538 


7 


54 


23535 


99348 


24186 


75814 


00652 


76465 


6 


55 


23607 


99346 


24261 


75739 


00654 


76393 


5 


56 


23679 


99344 


24335 


75665 


00656 


76321 


4 


57 


23752 


99342 


24410 


75590 


00658 


76248 


3 


58 


23823 


99340 


24484 


75516 


00660 


76177 


2 


59 


23895 


99337 


24558 


75442 


00663 


76105 


1 


60 


23967 


99335 


24632 


75368 


00665 


76033 
Secant. 




M. 




Co-sine. 


Sine. 


Co-tans:. 


Tansrent. 


Co-secant 



34 



80 De<rre<^. 



113 Artificial Sines, Tang, and Sec. 10 Degrees. 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 


60 




; o 


9.23967 


9.99335 


9.24632 


10.75368 


10.00665 


10.76033 




! 1 


24039 


99333 


24706 


75294 


00667 


75961 


59 




' 2 


24110 


99331 


24779 


75221 


00669 


75890 


58 




3 


24181 


99328 


24853 


75147 


00672 


75819 


57 




; 4 


24253 


99326 


24926 


75074 


00674 


75747 


56 




5 


24324 


99324 


25000 


75000 


00676 


75676 


55 




6 


24395 


99322 


25073 


74927 


00678 


75605 


54 




7 


24466 


99319 


25146 


74854 


00681 


75534 


53 




o 


24536 


99317 


25219 


74781 


00683 


75464 


52 




9 


24607 


99315 


25292 


74708 


00685 


75393 


51 




10 


9.24677 


9.99313 


9.25365 


10.74635 


10.00687 


10.75323 


50 




11 


24748 


99310 


25437 


74563 


00690 


75252 


49 




12 


24818 


99308 


25510 


74490 


00692 


75182 


48 




13 


24838 


99306 


25582 


74418 


00694 


75112 


47 




14 


24958 


99304 


25655 


74345 


00696 


75042 


46 




15 


25028 


99301 


25727 


74273 


00699 


74972 


45 




16 


25098 


99299 


25799 


74201 


00701 


74902 


44 




17 


25168 


99297 


25871 


74129 


00703 


74832 


43 




13 


25237 


99294 


25943 


74057 


00706 


74763 


42 




19 


25307 


99292 


26015 


73985 


00708 


74693 


41 




20 


9.25376 


9.99290 


9.26086 


10.73914 


10.00710 


10.74624 


40 




21 


25445 


99288 


26158 


73842 


00712 


74555 


39 




22 


25514 


99285 


26229 


73771 


00715 


74486 


38 




23 


25583 


99283 


26301 


73699 


00717 


74417 


37 




24 


25652 


99281 


26372 


73628 


00719 


74348 


36 




25 


25721 


99278 


26443 


73557 


00722 


74279 


35 




26 


25790 


99276 


26514 


73486 


00724 


74210 


34 




■ 27 


25858 


99274 


26585 


73415 


00726 


74142 


33 




28 


25927 


99271 


26655 


73345 


00729 


74073 


32 




29 


25995 


99269 


26726 


73274 


00731 


74005 


31 




30 


9.26063 


9.99267 


9.26797 


10.73203 


10.00733 


10.73937 


30 




31 


26131 


99264 


26867 


73133 


00736 


73869 


29 




32 


26199 


99262 


26937 


73063 


00738 


73801 


28 




33 


26267 


99260 


27008 


72992 


00740 


73733 


27 




34 


26335 


99257 


27078 


72922 


00743 


73665 


26 




35 


26403 


99255 


27143 


72852 


00745 


73597 


25 




36 


26470 


99252 


27218 


72782 


00748 


73530 


24 




1 37 


26538 


99250 


27288 


72712 


00750 


73462 


23 




1 38 


26605 


99248 


27357 


72643 


00752 


73395 


22 




: 39 


26672 


99245 


27427 


72573 


00755 


73328 
10.73261 


21 
20 




40 


9.26739 


9.99243 


9.27496 


10.72504 


10.00757 




41 


26806 


99241 


27566 


72434 


00759 


73194 


19 




42 


26873 


99238 


27635 


72365 


00762 


73127 


18 




43 


26940 


99236 


27704 


72296 


00764 


73060 


17 




44 


27007 


99233 


27773 


72227 


00767 


72993 


16 




45 


27073 


99231 


27842 


72158 


00769 


72927 


15 




46 


27140 


99229 


27911 


72089 


00771 


72860 


14 




47 


27206 


99226 


27980 


72020 


00774 


72794 


13 




48 


27273 


99224 


28049 


71951 


00776 


72727 


12 




49 


27339 


99221 


28117 


71883 


00779 


72661 


11 




50 


9.27405 


9.99219 


9.28186 


10.71814 


10.00781 


10.72595 


10 




51 


27471 


99217 


28254 


71746 


00783 


72529 


9 




52 


27537 


99214 


28323 


71677 


00786 


72463 


8 




53 


27602 


99212 


28391 


71609 


00788 


72398 


7 




54 


27668 


99209 


28459 


71541 


00791 


72332 


6 




55 


27734 


99207 


28527 


71473 


00793 


72266 


5 




56 


27799 


99204 


28595 


71405 


00796 


72201 


4 




57 


27864 


99202 


28662 


71338 


00798 


72136 


3 




58 


27930 


99200 


28730 


71270 


00800 


72070 


2 




59 


27995 


99197 


28798 


71202 


00803 


72005 


1 




60 


28060 


99195 


28865 


71135 


00805 


71940 









Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 





79 Degrees. 



Artificial Sines, Tang, and Sec. 11 Degrees. 119 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 


60 





9.28060 


9.99195 


9.28865 


10.71135 


10.00805 


10.71940 


1 


28125 


99192 


28933 


71067 


00808 


71875 


59 


2 


28190 


99190 


29000 


71000 


00810 


71810 


58 


3 


28254 


99187 


29067 


70933 


00813 


71746 


57 


4 


28319 


99185 


29134 


70866 


00815 


71681 


56 


5 


28384 


99182 


29201 


70799 


00818 


71616 


55 


6 


28448 


99180 


29268 


70732 


00820 


71552 


54 


7 


28512 


99177 


29335 


70665 


00823 


71488 


53 


8 


28577 


99175 


29402 


70598 


00825 


71423 


52 


9 


28641 


99172 


29468 


70532 


00828 


71359 


51 


10 


9.28705 


9.99170 


9.29535 


10.70465 


10.00830 


10.71295 


50 


11 


28769 


99167 


29601 


70399 


00833 


71231 


49 


12 


28833 


99165 


29668 


70332 


00835 


71167 


48 


13 


28896 


99162 


29734 


70266 


00838 


71104 


47 


14 


28960 


99160 


29800 


70200 


00840 


71040 


46 


15 


29024 


99157 


29866 


70134 


00843 


70976 


45 


16 


29087 


99155 


29932 


70068 


00845 


70913 


44 


17 


29150 


99152 


29998 


70002 


00848 


70850 


43 


18 


29214 


99150 


30064 


69936 


00850 


70786 


42 


19 


29277 


99147 
9.99145 


30130 
9.30195 


69870 


00853 


70723 
10.70660 


41 

40 


20 


9.29340 


10.69805 


10.00855 


21 


29403 


99142 


30261 


69739 


00858 


70597 


39 


22 


29466 


99140 


30326 


69674 


00860 


70534 


38 


23 


29529 


99137 


30391 


69609 


00863 


70471 


37 


24 


29591 


99135 


30457 


69543 


00865 


70409 


36 


25 


29654 


99132 


30522 


69478 


00868 


70346 


35 


26 


29716 


99130 


30587 


69413 


00870 


70284 


34 


27 


29779 


99127 


30652 


69348 


00873 


70221 


33 


28 


29841 


99124 


30717 


69283 


00876 


70159 


32 


29 


29903 


99122 


30782 


69218 


00878 


70097 


31 


30 


9.29966 


9.99119 


9.30846 


10.69154 


10.00881 


10.70034 


30 


31 


30028 


99117 


30911 


69089 


00883 


69972 


29 


32 


30090 


99114 


30975 


69025 


00886 


69910 


28 


33 


30151 


99112 


31040 


68960 


00888 


69849 


27 


34 


30213 


99109 


31104 


68896 


00891 


69787 


26 


35 


30275 


99106 


31168 


68832 


00894 


69725 


25 


36 


30336 


99104 


31233 


68767 


00896 


69664 


24 


37 


30398 


99101 


31297 


68703 


00899 


69602 


23 


38 


30459 


99099 


31361 


68639 


00901 


69541 


22 


39 


30521 


99096 


31425 
9.31489 


68575 


00904 


69479 


21 
~20" 


40 


9.30582 


9.99093 


10.68511 


10.00907 


10.69418 


41 


30643 


99091 


31552 


68448 


00909 


69357 


19 ! 


42 


30704 


99088 


31616 


68384 


00912 


69296 


18 


43 


30765 


99086 


31679 


68321 


00914 


69235 


17 


44 


30826 


99083 


31743 


68257 


00917 


69174 


16 


45 


30887 


99080 


31806 


68194 


00920 


69113 


15 


46 


30947 


99078 


31870 


68130 


00922 


69053 


14 


47 


31008 


99075 


31933 


68067 


00925 


68992 


13 


48 


31068 


99072 


31996 


68004 


00928 


68932 


12 


49 
50 


31129 


99070 


32059 


67941 


00930 


68871 


11 

"To" 


9.31189 


9.99067 


9.32122 


10.67878 


10.00933 


10.68811 


51 


31250 


99064 


32185 


67815 


00936 


68750 


9 


52 


31310 


99062 


32248 


67752 


00938 


68690 


8 


53 


31370 


99059 


32311 


67689 


00941 


68630 


7 


54 


31430 


99056 


32373 


67627 


00944 


68570 


6 


55 


31490 


99054 


32436 


67564 


00946 


68510 


5 


56 


31549 


99051 


32498 


67502 


00949 


68451 


4 


57 


31609 


99048 


32561 


67439 


00952 


68391 


3 


58 


31669 


99046 


32623 


67377 


00954 


68331 


2 


59 


31728 


99043 


32685 


67315 


00957 


68272 


1 


60 


31788 
Co-sine. 


99040 


32747 


67253 


00960 


68212 
Secant. 





Sine. 


Co-tang. 


Tangent. 


Co-secant 


M. 



78 Degrees. 



120 Artificial Sines, Tang, and Sec. 12 Degrees. 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 
10.00960 


Co-sccant 







9.31788 


9.99040 


9.32747 


10.67253 


10.68212 


60 


1 


31847 


99038 


32810 


67190 


00962 


68153 


59 


2 


31907 


99035 


32872 


67128 


00965 


68093 


58 


o 


31966 


99032 


32933 


67067 


00968 


68034 


57 


4 


32025 


99030 


32995 


67005 


00970 


67975 56 


5 


32084 


99027 


33057 


66943 


00973 


67916 


55 


6 


32143 


99024 


33119 


66881 


00976 


67857 


54 


7 


32202 


99022 


33180 


66820 


00978 


67798 


53 


8 


32261 


99019 


33242 


66758 


00981 


67739 


52 


9 


32319 


99016 


33303 


66697 


00984 


67681 
10.67622 


51 
50 


10 


9.32378 


9.99013 


9.33365 


10.66635 


10.00937 


11 


32437 


99011 


33426 


66574 


00989 


67563 


49 


12 


32495 


99008 


33437 


66513 


00992 


67505 


48 


13 


32553 


99005 


33548 


66452 


00995 


67447 


47 


14 


32612 


99002 


33609 


66391 


00998 


67388 


46 


15 


32670 


99000 


33670 


66330 


01000 


67330 


45 


16 


32728 


98997 


33731 


66269 


01003 


67272 


44 


17 


32786 


98994 


33792 


66208 


01006 


67214 


43 


18 


32844 


93991 


33853 


66147 


01009 


67156 


42 


19 


32902 


98989 


33913 


66037 


01011 


67096 


41 


20 


9.32960 


9.98986 


9.33974 


10.66026 


10.01014 


10.67040 


40 


21 


33013 


98983 


34034 


65966 


01017 


66982 


39 


22 


33075 


98980 


34095 


65905 


01020 


66925 


38 


23 


33133 


98978 


34155 


65845 


01022 


66867 


37 


24 


33190 


98975 


34215 


65785 


01025 


66810 


36 


2:3 


33248 


98972 


34276 


65724 


01028 


66752 


35 


. 20 


33305 


98969 


34336 


65664 


01031 


66695 


34 


27 


33362 


98967 


34396 


65604 


01033 


66638 


33 


23 


33420 


98964 


34456 


65544 


01036 


66580 


32 


29 


33477 


98961 


34516 


65484 


01039 


66523 


31 

30 


30 


9.33534 


9.98958 


9.34576 


10.65424 


10.01042 


10.66466 


31 


33591 


98955 


34635 


65365 


01045 


66409 


29 


32 


33647 


98953 


34695 


65305 


01047 


66353 


28 


33 


33704 


98950 


34755 


65245 


01050 


66296 


27 


34 


33761 


98947 


34814 


65186 


01053 


66239 


26 


35 


33818 


98944 


34874 


65126 


01056 


66182 


25 


36 


33874 


98941 


34933 


65067 


01059 


66126 


24 


37 


33931 


98938 


34992 


65008 


01062 


66069 


23 


38 


33987 


98936 


35051 


64949 


01064 


66013 


22 


39 


34043 


98933 


35111 


64889 


01007 


65957 


21 


40 


9.34100 


9.98930 


9.35170 


10.64830 


10.01070 


10.65900 


20 


41 


34156 


98927 


35229 


64771 


01073 


65844 


19 


42 


34212 


98924 


35288 


64712 


01076 


65788 


18 


43 


34263 


98921 


35347 


64653 


01079 


65732 


17 


44 


34324 


98919 


35405 


64595 


01081 


65676 


16 


45 


34380 


98916 


35464 


64536 


01084 


65620 


15 


46 


34436 


98913 


35523 


64477 


01037 


65564 


14 


47 


34491 


98910 


35581 


64419 


01090 


65509 


13 


43 


34547 


98907 


35640 


64360 


01093 


65453 


12 


49 


34602 


98904 


35698 


64302 


01096 


65398 


11 


50 


9.34658 


9.98901 


9.35757 


10.64243 


10.01099 


10.65342 


10 


51 


34713 


98898 


35815 


64185 


01102 


65287 


9 


52 


34769 


98896 


35873 


64127 


01104 


65231 


8 


53 


34824 


98893 


35931 


64069 


01107 


65176 


7 


54 


34879 


98890 


35989 


64011 


OHIO 


65121 


6 


55 


34934 


98887 


36047 


63953 


01113 


65066 


5 


56 


34989 


93884 


36105 


63895 


01116 


65011 


4 


57 


35044 


98881 


36163 


63837 


01119 


64956 


3 


58 


35099 


98878 


36221 


63779 


01122 


64901 


2 


59 


35154 


98875 


36279 


63721 


01125 


64846 


1 


60 


35209 


98872 


36336 


63664 


01128 


64791 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 



77 Degrees. 



Artificial Sines, Tang, and Sec. 13 Degrees. 121 






Sine. 
9.35209 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 
10.64791 


60 


9.98872 


9.36336 


10.63664 


10.01128 


1 


35263 


98869 


36394 


63606 


01131 


64737 


59 


2 


35318 


98867 


36452 


63548 


01133 


64682 


58 


3 


35373 


98864 


36509 


63491 


01136 


64627 


57 


4 


35427 


98861 


36566 


63434 


01139 


64573 


56 


5 


35481 


98858 


36624 


63376 


01142 


64519 


55 


6 


35536 


98855 


36681 


63319 


01145 


64464 


54 


1 7 


35590 


98852 


36738 


63262 


01148 


64410 


53 


i 8 


35644 


98849 


36795 


63205 


01151 


64356 


52 


i 9 


35698 


98846 


36852 
9.36909 


63148 


01154 


64302 


51 


10 


9.35752 


9.98843 


10.63091 


10.01157 


10.64248 


50 


i u 


35806 


98840 


36966 


63034 


01160 


64194 


49 


1 12 


35860 


98837 


37023 


62977 


01163 


64140 


48 


1 13 


35914 


98834 


37080 


62920 


01166 


64086 


47 


14 


35968 


98831 


37137 


62863 


01169 


64032 


46 


15 


36022 


98828 


37193 


62807 


01172 


63978 


45 


16 


36075 


98825 


37250 


62750 


01175 


63925 


44 


17 


36129 


98822 


37306 


62694 


01178 


63871 


43 


18 


36182 


98819 


37363 


62637 


01181 


63818 


42 


I 19 


36236 


98816 


37419 


62581 


01184 
10.01187 


63764 


41 
40 


1 20 


9.36289 


9.98813 


9.37476 


10.62524 


10.63711 


1 21 


36342 


98810 


37532 


62468 


01190 


63658 


39 


22 


36395 


98807 


37588 


62412 


01193 


63605 


38 


23 


36449 


98804 


37644 


62356 


01196 


63551 


37 


24 


36502 


98801 


37700 


62300 


01199 


63498 


36 


25 


36555 


9879S 


37756 


62244 


01202 


63445 


35 


1 26 


36608 


98795 


37812 


62188 


01205 


63392 


34 


1 27 


36660 


98792 


37868 


62132 


01208 


63340 


33 


28 


36713 


98789 


37924 


62076 


01211 


63287 


32 


! 29 
30 


36766 
9.36819 


98786 


37980 


62020 


01214 
10.01217 


63234 
10.63181 


31 
"30 


9.98783 


9.38035 


10.61965 


31 


36871 


98780 


38091 


61909 


01220 


63129 


29 


32 


36924 


98777 


38147 


61853 


01223 


63076 


28 


33 


36976 


98774 


38202 


61798 


01226 


63024 


27 


34 


37028 


98771 


38257 


61743 


01229 


62972 


26 


1 35 


37081 


98768 


38313 


61687 


01232 


62919 


25 


1 36 


37133 


98765 


38368 


61632 


01235 


62867 


24 


37 


37185 


98762 


38423 


61577 


01238 


62815 


23 


38 


37237 


98759 


38479 


61521 


01241 


62763 


22 


39 


37289 


98756 


38534 


61466 


01244 
10.01247 


62711 


21 


40 


9.37341 


9.98753 


9.38589 


10.61411 


10.62659 


20 


41 


37393 


98750 


38644 


61356 


01250 


62607 


19 


42 


37445 


98746 


38699 


61301 


01254 


62555 


IS 


43 


37497 


98743 


38754 


61246 


01257 


62503 


17 


44 


37549 


98740 


38808 


61192 


01260 


62451 


16 | 

15 

14 


45 


37600 


98737 


38863 


61137 


01263 


62400 


46 


37652 


98734 


38918 


61082 


01266 


62348 


47 


37703 


98731 


38972 


61028 


01269 


62297 


13 


48 


37755 


98728 


39027 


60973 


01272 


62245 


12 


49 


37806 


98725 


39082 


60918 


01275 


62194 
10.62142 


11 


50 


9.37858 


9-98722 


9.39136 


10.60864 


10.01278 


10 


51 


37909 


98719 


39190 


60810 


01281 


62091 


9 


52 


37960 


98715 


39245 


60755 


01285 


62040 


8 


53 


38011 


98712 


39299 


60701 


01288 


61989 


7 


54 


38062 


98709 


39353 


60647 


01291 


61938 


6 


55 


38113 


98706 


39407 


60593 


01294 


61887 


5 


56 


38164 


98703 


39461 


60539 


01297 


61836 


4 


57 


38215 


98700 


39515 


60485 


01300 


61785 


3 


58 


38266 


98697 


39569 


60431 


01303 


61734 


2 


59 


38317 


98694 


39623 


60377 


01306 


61683 


1 


60 


38368 


98690 


39677 


60323 


01310 


61632 


| 
M.| 


| j Co-sine. 


Sine. 


Co- tang. 


Tangent. 


Co-secant 


Secant. 



34* 



76 Degrees. 



122 Artificial Sines, Tang, and Sec. 14 Degrees*. 



M. 




Sine. 
9.38368 


Co-sine. 
9.98690 


Tangent. 


Co-tang. 


Secant. 


Co-secant 


60 


9.39677 


10.60323 


10.01310 


10.61632 


1 


38418 


98687 


39731 


60269 


01313 


61582 


59 


2 


38469 


98684 


39785 


60215 


01316 


61531 


58 


3 


38519 


98681 


39833 


60162 


01319 


61481 


57 ! 


4 


33570 


98678 


39892 


60108 


01322 


61430 


5C 


5 


38620 


98675 


39945 


60055 


01325 


61380 


55 


6 


33670 


98671 


39999 


60001 


01329 


61330 


54 


7 


38721 


98663 


40052 


59948 


01332 


61279 


53 i 


8 


38771 


98665 


40106 


59894 


01335 


61229 


52 


9 


38821 


98662 


40159 


59841 


01338 


61179 
10.61129 


51 
50 


10 


9.38871 


9.98659 


9.40212 


10.59788 


10.01341 


11 


38921 


98656 


40266 


59734 


01344 


61079 


49 


12 


38971 


98652 


40319 


59681 


01348 


61029 


48 


13 


39021 


98649 


40372 


59628 


01351 


60979 


47 


14 


39071 


98646 


40425 


59575 


01354 


60929 


46 


15 


39121 


98643 


40478 


59522 


01357 


60879 


45 


16 


39170 


98640 


40531 


59469 


01360 


60830 


44 


•1 


39220 


98636 


40584 


59416 


01364 


60780 


43 


18 


39270 


98633 


40636 


59364 


01367 


60730 


42 


19 
20 


39319 
9.39369 


98630 
9.98627 


40689 


59311 
10.59258 


01370 


60681 


41 

40 


9.40742 


10.01373 


10.60631 


21 


39418 


98623 


40795 


59205 


01377 


60582 


39 


22 


39467 


98620 


40847 


59153 


01380 


60533 


38 


23 


39517 


98617 


40900 


59100 


01383 


60483 


37 


24 


39566 


98614 


40952 


59048 


01386 


60434 


36 


25 


39615 


98610 


41005 


58995 


01390 


60385 


35 


26 


39664 


98607 


41057 


58943 


01393 


60336 


34 


27 


39713 


98604 


41109 


58891 


01396 


60287 


33 
32 


28 


39762 


98601 


41161 


58839 


01399 


60238 


29 


39811 


98597 


41214 


58786 


01403 


60189 


31 

30 


30 


9.39860 


~ 9. 93594 


9.41266 


10.58734 


10.01406 


10.60140 


31 


39909 


98591 


41318 


58682 


01409 


60091 


29 


32 


39958 


98583 


41370 


58630 


01412 


60042 


28 


33 


40006 


98584 


41422 


58578 


01416 


59994 


27 


34 


40055 


98581 


41474 


58526 


01419 


59945 


26 


35 


40103 


98578 


41526 


58474 


01422 


59897 


25 


36 


40152 


98574 


41578 


58422 


01426 


59848 


24 


37 


40200 


98571 


41629 


58371 


01429 


59800 


23 


; 38 


40249 


98568 


41681 


58319 


01432 


59751 


22 


39 


40297 


98565 


41733 


58267 


01435 


59703 


21 
~20 


40 


9.40346 


9.98561 


9.41784 


10.58216 


10.01439 


10.59654 


41 


40394 


98558 


41836 


58164 


01442 


59606 


19 


42 


40442 


98555 


41887 


58113 


01445 


59558 


18 


43 


40490 


98551 


41939 


58061 


01449 


59510 


17 


44 


40538 


98548 


41990 


58010 


01452 


59462 


16 


45 


40586 


98545 


42041 


57959 


01455 


59414 


15 


46 


40634 


93541 


42093 


57907 


01459 


59366 


14 


47 


40682 


98538 


42144 


57856 


01462 


59318 


13 


48 


40730 


98535 


42195 


57805 


01465 


59270 


12 


49 


40778 


98531 


42246 


57754 


01469 


59222 
10.59175 


11 
10 


50 


9.40825 


9.98523 


9.42297 


10.57703 


10.01472 


51 


40373 


98525 


42348 


57652 


01475 


59127 


9 


52 


40921 


98521 


42399 


57601 


01479 


59079 


8 


53 


40968 


98518 


42450 


57550 


01482 


59032 


7 


54 


41016 


98515 


42501 


57499 


01485 


58984 


6 


55 


41063 


98511 


42552 


57448 


01489 


58937 


5 


56 


41111 


98508 


42603 


57397 


01492 


53889 


4 


57 


41158 


98505 


42653 


57347 


01495 


58842 


3 


58 


41205 


98501 


42704 


57296 


01499 


58795 


2 


59 


41252 


98498 


42755 


57245 


01502 


58748 


1 


60 


41300 


98494 


42805 


57195 


01506 


58700 




M7 




Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 



Tfi Degrees 



Artificial Sines, Tang, and Sec. 15 Degrees. 123 



M. 



Sine. 
9.41300 


Co-sine. 


Tangent. 


Co-tang. 
10.57195 


Secant. 


Co-secant 


60 


9,98494 


9.42805 


10.01506 


10.58700 


1 


41347 


98491 


42856 


57144 


01509 


58653 


59 


2 


41394 


98488 


42906 


5^094 


01512 


58606 


58 


3 


41441 


98484 


42957 


57043 


01516 


58559 


57 


4 


41488 


98481 


43007 


56993 


01519 


58512 


56 


5 


41535 


98477 


43057 


56943 


01523 


58465 


55 


6 


41582 


98474 


43108 


56892 


01526 


58418 


54 


7 


41628 


98471 


43158 


56842 


01529 


58372 


53 


8 


41675 


98467 


43208 


56792 


01533 


58325 


52 


9 


41722 


98464 
9.98460 


43258 


56742 
10.56692 


01536 
10.01540 


58278 
10.58232 


51 
50 


10 


9.41783 


9.43308 


11 


41815 


98457 


43358 


56642 


01543 


58185 


49 


12 


41851 


98453 


43408 


56592 


01547 


58139 


48 


13 


41908 


98450 


43458 


56542 


01550 


58092 


47 


14 


41954 


98447 


43508 


56492 


01553 


58046 


46 


15 


42001 


98443 


43558 


56442 


01557 


57999 


45 


16 


42047 


98440 


43607 


56393 


01560 


57953 


44 


■ 17 


42093 


98436 


43657 


56343 


01564 


57907 


43 


18 


42140 


98433 


43707 


56293 


01567 


57860 


42 


19 


42186 


98429 


43756 


56244 


01571 


57814 


41 


20 


9.42232 


9.98426 


9.43806 


10.56194 


10.01574 


10.57768 


40 


21 


42278 


98422 


43855 


56145 


01578 


57722 


39 


22 


42324 


98419 


43905 


56095 


01581 


57676 


38 


23 


42370 


98415 


43954 


56046 


01585 


57630 


37 


24 


42416 


98412 


44004 


55996 


01588 


57584 


36 


25 


42461 


98409 


44053 


55947 


01591 


57539 


35 


26 


42507 


98405 


44102 


55898 


01595 


57493 


34 


27 


42553 


98402 


44151 


55849 


01598 


57447 


33 


28 


42599 


98398 


44201 


55799 


01602 


57401 


32 


29 


42644 


98395 


44250 


55750 


01605 


57356 


31 


30 


9.42690 


9.98391 


9.44299 


10.55701 


10.01609 


10.57310 


30 


31 


42735 


98388 


44348 


55652 


01612 


57265 


29 


32 


42781 


98384 


44397 


55603 


01616 


57219 


28 


33 


42826 


98381 


44446 


55554 


01619 


57174 


27 


34 


42872 


98377 


44495 


55505 


01623 


57128 


26 


35 


42917 


98373 


44544 


55456 


01627 


57083 


25 


36 


42962 


98370 


44592 


55408 


01630 


57038 


24 


37 


43008 


98366 


44641 


55359 


01634 


56992 


23 


38 


43053 


98363 


44690 


55310 


01637 


56947 


22 


39 
40 


43098 
9.43143 


98359 


44738 


55262 
10.55213 


01641 


56902 


21 


9.98356 


9.44787 


10.01644 


10.56857 


20 


41 


43188 


98352 


44836 


55164 


01648 


56812 


19 . 


42 


43233 


98349 


44884 


55116 


01651 


56767 


18 


43 


43278 


98345 


44933 


55067 


01655 


56722 


17 


44 


43323 


98342 


44981 


55019 


01658 


56677 


16 


45 


43367 


98338 


45029 


54971 


01662 


56633 


15 


46 


43412 


98334 


45078 


54922 


01666 


56588 


14 


47 


43457 


98331 


45126 


54874 


01669 


56543 


13 


48 


43502 


98327 


45174 


54826 


01673 


56498 


12 


49 


43546 


98324 


45222 


54778 


01676 


56454 


11 


50 


9.43591 


9.98320 


9.45271 


10.54729 


10.01680 


10.56409 


10 


51 


43635 


98317 


45319 


54681 


01683 


56365 


9 ' 


52 


43680 


98313 


45367 


54633 


01687 


56320 


8 


53 


43724 


98309 


45415 


54585 


01691 


56276 


7 


54 


43769 


98306 


45463 


54537 


01694 


56231 


6 


55 


43813 


98302 


45511 


54489 


01698 


56187 


5 


56 


43857 


98299 


45559 


54441 


01701 


56143 


4 


57 


43901 


98295 


45606 


54394 


01705 


56099 


3 


58 


43946 


98291 


45654 


54346 


01709 


56054 


2 


59 


43990 


98288 


45702 


54298 


01712 


56010 


1 


60 


44034 


98284 


45750 


54250 


01716 


55966 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 



74 Degrees 



124 Artificial Sines, Tang, and Sec. 16 Degrees. 





M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 











9.44034 


9.98284 


9.45750 


10.54250 


10.01716 


10.55966 


60 






1 


44078 


98281 


45797 


54203 


01719 


55922 


59 






2 


44122 


98277 


45845 


54155 


01723 


55878 


58 






3 


44166 


98273 


45892 


54108 


01727 


55834 


57 






4 


44210 


98270 


45940 


54060 


01730 


55790 


56 






5 


44253 


98266 


45987 


54013 


01734 


55747 


55 






6 


44297 


98262 


46035 


53965 


01738 


55703 


54 






7 


44341 


98259 


46082 


53918 


01741 


55659 


53 






8 


44385 


98255 


46130 


53870 


01745 


55615 


52 






9 


44428 


98251 


46177 


53823 


01749 


55572 
10.55528 


51 
50 






10 


9.44472 


9.98248 


9.46224 


10.53776 


10.01752 






11 


44516 


98244 


46271 


53729 


01756 


55484 


49 






12 


44559 


98240 


46319 


53681 


01760 


55441 


48 






13 


44602 


98237 


46366 


53634 


01763 


55398 


47 






14 


44646 


98233 


46413 


53587 


01767 


55354 


46 






15 


44689 


98229 


46460 


53540 


01771 


55311 


45 






16 


44733 


98226 


46507 


53493 


01774 


55267 


44 






17 


44776 


98222 


46554 


53446 


01778 


55224 


43 






18 


44819 


98218 


46601 


53399 


01782 


55181 


42 






19 


44862 


98215 


46648 


53352 


01785 


55138 


41 






20 


9.44905 


9.98211 


9.46694 


10.53306 


10.01789 


10.55095 


40 






21 


44948 


98207 


46741 


53259 


01793 


55052 


39 






22 


44992 


98204 


46788 


53212 


01796 


55008 


38 






23 


45035 


98200 


46835 


53165 


01800 


54965 


37 






24 


45077 


98196 


46881 


53119 


01804 


54923 


36 






25 


45120 


98192 


46928 


53072 


01808 


54880 


35 






26 


45163 


98189 


46975 


53025 


01811 


54837 


34 






27 


45206 


98185 


47021 


52979 


01815 


54794 


33 






28 


45249 


98181 


47068 


52932 


01819 


54751 


32 






29 


45292 


98177 


47114 


52886 
10.52840 


01823 
10.01826 


54708 


31 






30 


9.45334 


9.98174 


9.47160 


10.54666 


30 






31 


45377 


98170 


47207 


52793 


01830 


54623 


29 






32 


45419 


98166 


47253 


52747 


01834 


54581 


28 






33 


45462 


98162 


47299 


52701 


01838 


54538 


27 






34 


45504 


98159 


47346 


52654 


01841 


54496 


26 






35 


45547 


98155 


47392 


52603 


01345 


54453 


25 






36 


45589 


98151 


47433 


52562 


01849 


54411 


24 






37 


45632 


98147 


47484 


52516 


01853 


54368 


23 






38 


45674 


98144 


47530 


52470 


01856 


54326 


22 






39 


45716 


98140 


47576 


52424 


01860 


54284 


21 






40 


9.45758 


9.98136 


9.47622 


10.52378 


10.01864 


10.54242 


20 






41 


45801 


98132 


47668 


52332 


01868 


54199 


19 






42 


45843 


98129 


47714 


52286 


01871 


54157 


18 






43 


45885 


98125 


47760 


52240 


01875 


54115 


17 






44 


45927 


98121 


47806 


52194 


01879 


54073 


16 






45 


45969 


98117 


47852 


52148 


01883 


54031 


15 






46 


46011 


98113 


47897 


52103 


01887 


53989 


14 






47 


46053 


98110 


47943 


52057 


01890 


53947 


13 






48 


46095 


98106 


47989 


52011 


01894 


53905 


12 






49 


46136 


98102 


48035 


51965 


01898 


53864 


11 
10 






50 


9.46178 


9.98098 


9.48080 


10.51920 


10.01902 


10.53822 






51 


46220 


98094 


48126 


51874 


01906 


53780 


9 






52 


46262 


98090 


48171 


51829 


01910 


53738 


8 






53 


46303 


98087 


48217 


51783 


01913 


53697 


7 






54 


46345 


98083 


48262 


51738 


01917 


53655 


6 






55 


46386 


98079 


48307 


51693 


01921 


53614 


5 






56 


46428 


98075 


48353 


51647 


01925 


53572 


4 






57 


46469 


98071 


48398 


51602 


01929 


53531 


3 






58 


46511 


98067 


48443 


51557 


01933 


53489 


2 






59 


46552 


98063 


48489 


51511 


01937 


53448 


1 






60 


46594 


98060 


48534 


51466 


01940 


53406 











Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 





73 Degrees 



Artificial Sines, Tang, and Sec. 17 Degrees. 125 





Al. 


Sine. 


Co-sine. | 
9-98060 


i augent. 


Co-tang. 


Secant. 


Co-secant 









9.46594 


9.48534 


10.51466 


10.01940 


10.53406 


60 




1 


46635 


98056 


48579 


51421 


01944 


53365 


59 




2 


46676 


98052 


48624 


51376 


01948 


53324 


58 




3 


46717 


98048 


48669 


51331 


01952 


53283 


57 




4 


46758 


98044 


48714 


51286 


01956 


53242 


56 




5 


46800 


98040 


48759 


51241 


01960 


53200 


55 




6 


46841 


98036 


48804 


51196 


01964 


53159 


54 




7 


46882 


98032 


48849 


51151 


01968 


53118 


53 




8 


46923 


98029 


48894 


51106 


01971 


53077 


52 




9 


46964 


98025 


48939 


51061 
10.51016 


01975 


53036 
10.52995 


51 

50 




10 


9.47005 


9.98021 


9.48984 


10.01979 




11 


47045 


98017 


49029 


50971 


01983 


52955 


49 




12 


47086 


98013 


49073 


50927 


01987 


52914 


48 




13 


47127 


98009 


49118 


50882 


01991 


52873 


47 




14 


47168 


98005 


49163 


50837 


01995 


52832 


46 




15 


47209 


98001 


49207 


50793 


01999 


52791 


45 




16 


47249 


97997 


49252 


50748 


02003 


52751 


44 




17 


47290 


97993 


49296 


50704 


02007 


52710 


43 




18 


47330 


97989 


49341 


50659 


02011 


52670 


42 




19 


47371 


97986 


49385 


50615 


02014 


52629 


41 




20 


9.47411 


9.97982 


9.49430 


10.50570 


10.02018 


10.52589 


40 




21 


47452 


97978 


49474 


50526 


02022 


52548 


39 




22 


47492 


97974 


49519 


50481 


02026 


52508 


38 




23 


47533 


97970 


49563 


50437 


02030 


52467 


37 




24 


47573 


97966 


49607 


50393 


02034 


52427 


36 




25 


47613 


97962 


49652 


50348 


02038 


52387 


35 




26 


47654 


97958 


49696 


50304 


02042 


52346 


34 




27 


47694 


97954 


49740 


50260 


02046 


52306 


33 




28 


47734 


97950 


49784 


50216 


02050 


52266 


32 




29 


47774 


97946 


49828 


50172 


02054 


52226 


31 
30 




30 


9.47814 


9.97942 


9.49872 


10.50128 


10.02058 


10.52186 




31 


47854 


97938 


49916 


50084 


02062 


52146 


29 




32 


47894 


97934 


49960 


50040 


02066 


52106 


28 




33 


47934 


97930 


50004 


49996 


02070 


52066 


27 




34 


47974 


97926 


50048 


49952 


02074 


52026 


26 




35 


48014 


97922 


50092 


49908 


02078 


51986 


25 




36 


48054 


97918 


50136 


49864 


02082 


51946 


24 




37 


48094 


97914 


50180 


49820 


02086 


51906 


23 




38 


48133 


97910 


50223 


49777 


02090 


51867 


22 




39 
40 


48173 
9.48213 


97906 


50207 


49733 


02094 


51827 


21 




9.97902 


9.50311 


10.49689 


10.02098 


10.51787 


20 




41 


48252 


97898 


50355 


49645 


02102 


51748 


19 




42 


48292 


97894 


50398 


49602 


02106 


51708 


18 




43 


48332 


97890 


50442 


49558 


02110 


51668 


17 




44 


48371 


97886 


50485 


49515 


02114 


51629 


16 




45 


48411 


97882 


50529 


49471 


02118 


51589 


15 




46 


48450 


97878 


50572 


49428 


02122 


51550 


14 




47 


48490 


97874 


50616 


49384 


02126 


51510 


13 




48 


48529 


97870 


50659 


49341 


02130 


51471 


12 




49 
50 


48568 
9.48607 


97866 


50703 


49297 


02134 


51432 


11 




9.97861 


9.50746 


10.49254 


10.02139 


10.51393 


10 




51 


48647 


97857 


50789 


49211 


02143 


51353 


9 




52 


48686 


97853 


50833 


49167 


02147 


51314 


8 




53 


48725 


97849 


50876 


49124 


02151 


51275 


7 




54 


48764 


97845 


50919 


49081 


02155 


51236 


6 




55 


48803 


97841 


50962 


49038 


02159 


51197 


5 




56 


48842 


97837 


51005 


48995 


02163 


51158 


4 




57 


48881 


97833 


51048 


48952 


02167 


51119 


3 




58 


48920 


97829 


51092 


48908 


02171 


51080 


2 




59 


48959 


97825 


51135 


48865 


02175 


51041 


1 




60 


48998 


97821 


51178 


48822 


02179 


51002 







1 Co-sine. 


Sine. 


1 Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 



72 Degrees. 



126 Artificial Sines, Tang, and °ec. 18 Degrees. 



|m. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. | 


Co-secant 




S o 


9.48998 


9.97821 


9.51178 


10.48822 


10.02179 


10.51002 


60 


1 


49037 


97817 


51221 


48779 


02183 


50963 


59 


2 


49076 


97812 


51264 


48736 


02188 


50924 


58 


3 


49115 


97808 


51306 


48694 


02192 


50885 


57 


4 


49153 


97804 


51349 


48651 


02196 


50847 


56 


5 


49192 


97800 


51392 


48608 


02200 


50808 


55 


6 


49231 


97796 


51435 


48565 


02204 


50769 


54 


7 


49269 


97792 


51478 


48522 


02208 


50731 


53 


8 


49308 


97788 


51520 


48480 


02212 


50692 


52 


9 


49347 


97784 


51563 


48437 


02216 


50653 


51 

50 


10 


9.49385 


9.97779 


9-51606 


10.48394 


10.02221 


10.50615 


11 


49424 


97775 


51648 


48352 


02225 


50576 


49 


12 


49462 


97771 


51691 


48309 


02229 


50538 


48 


13 


49500 


97767 


51734 


48266 


02233 


50500 


47 


14 


49539 


97763 


51776 


48224 


02237 


50461 


46 


15 


49577 


97759 


51819 


48181 


02241 


50423 


45 


16 


49615 


97754 


51861 


48139 


02246 


50385 


44 


17 


49654 


97750 


51903 


48097 


02250 


50346 


43 


18 


49692 


97746 


51946 


48054 


02254 


50308 


42 


19 


49730 


97742 


51983 


48012 


02258 


50270 


41 


20 


9.49768 


9.97738 


9.52031 


10.47969 


10.02262 


10.50232 


40 


21 


49806 


97734 


52073 


47927 


02266 


50194 


39 


22 


49844 


9772^ 


52115 


47885 


02271 


50156 


38 


23 


49882 


97725 


52157 


47843 


02275 


50118 


37 


24 


49920 


97721 


52200 


47800 


02279 


50080 


36 


25 


49958 


97717 


52242 


47758 


02283 


50042 


35 


26 


49996 


97713 


52284 


47716 


02287 


50004 


34 


27 


50034 


97708 


52326 


47674 


02292 


49966 


33 


28 


50072 


97704 


52368 


47632 


02296 


49928 


32 


29 


50110 


97700 


52410 


47590 


02300 


49890 


31 
30 


30 


9.50148 


9.97696 


9.52452 


10.47548 


10.02304 


10.49852 


31 


50185 


97691 


52494 


47506 


02309 


49815 


29 


32 


50223 


97687 


52536 


47464 


02313 


49777 


28 


33 


50261 


97683 


52578 


47422 


02317 


49739 


27 


34 


50298 


97679 


52620 


47380 


02321 


49702 


26 


35 


50336 


97674 


52661 


47339 


02326 


49664 


25 


36 


50374 


97670 


52703 


47297 


02330 


49626 


24 


37 


50411 


97666 


52745 


47255 


02334 


49589 


23 


38 


50449 


97662 


52787 


47213 


02338 


49551 


22 


39 


50486 


97657 


52829 
9.52870 


47171 


02343 


49514 


21 

20 


40 


9.50523 


9.97653 


10.47130 


10.02347 


10.49477 


41 


50561 


97649 


52912 


47088 


02351 


49439 


19 


42 


50598 


97645 


52953 


47047 


02355 


49402 


18 


43 


50635 


97640 


52995 


47005 


02360 


49365 


17 


44 


50673 


97636 


53037 


46963 


02364 


49327 


16 


45 


50710 


97632 


53078 


46922 


02368 


49290 


15 


46 


50747 


97628 


53120 


46880 


02372 


49253 


14 


47 


50784 


97623 


53161 


46839 


02377 


49216 


13 


48 


50821 


97619 


53202 


46798 


02381 


49179 


12 


49 


50858 


97615 


53244 


46756 


02385 


49142 


11 


50 


9.50896 


9.97610 


9.53285 


10.46715 


10.02390 


10 49104 


10 


51 


50933 


97606 


53327 


46673 


02394 


49067 


9 


52 


50970 


97602 


53368 


46632 


02398 


49030 


G 


53 


51007 


97597 


53409 


46591 


02403 


48993 


7 


54 


51043 


97593 


53450 


46550 


02407 


48957 


6 


55 


51080 


97589 


53492 


46508 


02411 


48920 


5 


56 


51117 


97584 


53533 


46467 


02416 


48883 


4 


57 


51154 


97580 


53574 


46426 


02420 


48846 


3 


58 


51191 


97576 


53615 


46385 


02424 


48809 


2 


59 


51227 


97571 


53656 


46344 


02429 


48773 


1 


, 60 


51264 


97567 


53697 


46303 


02433 


48736 





I' 


Co-sine. 


Sine. 


Co-tan?. 


Tangent. 


Co-secant 


Secant. 


M. 



71 Decrees. 







Artificial Sines, Tang. 


and Sec. 19 De 


grees. 


127 




M. 


Sine. 


Co-sine. 
9.97567 


Tangent. 


Co-tang. 


Secant. 


Co-secant | | 







9.51264 


9.53697 


10.46303 


10.02433 


10.48736 


60 




1 


51301 


97563 


53738 


46262 


02437 


48699 


59 




2 


51338 


97558 


53779 


46221 


02442 


48662 


58 




3 


51374 


97554 


53820 


46180 


02446 


48626 


57 




4 


51411 


97550 


53861 


46139 


02450 


48589 


56 




5 


51447 


97545 


53902 


46098 


02455 


48553 


55 




6 


51484 


97541 


53943 


46057 


02459 


48516 


54 




7 


51520 


97536 


53984 


46016 


02464 


48480 


53 




8 


51557 


97532 


54025 


45975 


02468 


48443 


52 




9 


51593 


97528 


54065 


45935 


02472 


48407 


51 




10 


9.51629 


9.97523 


9.54106 


10.45894 


10.02477 


10.48371 


50 




11 


51666 


97519 


54147 


45853 


02481 


48334 


49 




12 


51702 


97515 


54187 


45813 


02485 


48298 


48 




13 


51738 


97510 


54228 


45772 


02490 


48262 


47 




14 


51774 


97506 


54269 


45731 


02494 


48226 


46 




15 


51811 


97501 


54309 


45691 


02499 


48189 


45 




16 


51847 


97497 


54350 


45650 


02503 


48153 


44 




17 


51883 


97492 


54390 


45610 


02508 


48117 


43 




18 


51919 


97488 


54431 


45569 


02512 


48081 


42 




19 


51955 


97484 


54471 


45529 


02516 


48045 


41 
40 




20 


9.51991 


9.97479 


9.54512 


10.45488 


10.02521 


10.48009 




21 


52027 


97475 


54552 


45448 


02525 


47973 


39 




22 


52063 


97470 


54593 


45407 


02530 


47937 


38 




23 


52099 


97466 


54633 


45367 


02534 


47901 


37 




24 


52135 


97461 


54673 


45327 


02539 


47865 


36 




25 


52171 


97457 


54714 


45286 


02543 


47829 


35 




26 


52207 


97453 


54754 


45246 


02547 


47793 


34 




27 


52242 


97448 


54794 


45206 


02552 


47758 


33 




28 


52278 


97444 


54835 


45165 


02556 


47722 


32 : 




29 


52314 


97439 


54875 


45125 


02561 


47686 


31 




30 


9.52350 


9.97435 


9.54915 


10.45085 


10.02565 


10.47650 


30 ' 




31 


52385 


97430 


54955 


45045 


02570 


47615 


29 




32 


52421 


97426 


54995 


45005 


02574 


47579 


28 




33 


52456 


97421 


55035 


44965 


02579 


47544 


27 




34 


52492 


97417 


55075 


44925 


02583 


47508 


26 




35 


52527 


97412 


55115 


44885 


02588 


47473 


25 




36 


52563 


97408 


55155 


44845 


02592 


47437 


24 




37 


52598 


97403 


55195 


44805 


02597 


47402 


23 




38 


52634 


97399 


55235 


44765 


02601 


47366 


22 




39 


52669 


97394 


55275 


44725 


02606 


47331 
10.47295 


21 




40 


9.52705 


9.97390 


9.55315 


10.44685 


10.02610 


20 




41 


52740 


97385 


55355 


44645 


02615 


47260 


19 




42 


52775 


97381 


55395 


44605 


02619 


47225 


18 




43 


52811 


97376 


55434 


44566 


02624 


47189 


17 




44 


52846 


97372 


55474 


44526 


02628 


47154 


16 




45 


52881 


97367 


55514 


44486 


02633 


47119 


15 




46 


52916 


97363 


55554 


44446 


02637 


47084 


14 




47 


52951 


97358 


55593 


44407 


02642 


47049 


13 




48 


52986 


97353 


55633 


44367 


02647 


47014 


12 




49 


53021 


97349 


55673 


44327 


02651 


46979 


11 




50 


9.53056 


9.97344 


9.55712 


10.44288 


10.02656 


10.46944 


10 




51 


53092 


97340 


55752 


44248 


02660 


46908 


9 




52 


53126 


97335 


55791 


44209 


02665 


46874 


8 




53 


53161 


97331 


55831 


44169 


02669 


46839 


7 




54 


53196 


97326 


55870 


44130 


02674 


46804 


6 




55 


53231 


97322 


55910 


44090 


02678 


46769 


5 




56 


53266 


97317 


55949 


44051 


02683 


46734 


4 




57 


53301 


97312 


55989 


44011 


02688 


46699 


3 




58 


53336 


97308 


56028 


43972 


02692 


46664 


2 




59 


53370 


97303 


56067 


43933 


02697 


46630 


1 




60 


53405 


97299 


56107 


43893 


02701 


46595 




M. 






Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 



70 Degrees 



128 Artificial Sines, Tang, and Sec. 20 Degrees. 



ivi. 



Sine. 
9 53405 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 
10.02701 


Co-secant 


~W 




9.97299 


9.56107 


10.43893 


10.46595 




1 


53440 


97294 


56146 


43854 


02706 


46560 


59 




2 


53475 


97289 


56185 


43815 


02711 


46525 


58 




3 


53509 


97285 


56224 


43776 


02715 


46491 


57 




4 


53544 


97280 


56264 


43736 


02720 


46456 


56 




5 


53578 


97276 


56303 


43697 


02724 


46422 


55 




6 


53613 


97271 


56342 


43658 


2729 


46387 


54 




7 


53647 


97266 


56381 


43619 


£734 


46353 


53 




8 


53682 


97262 


:6420 


43580 


02738 


46318 


52 




9 


53716 


97257 


56459 


43541 


02743 


46284 


51 




10 


9.53751 


9.97252 


9.56498 


10.43502 


10.02748 


10.46249 


50 




11 


53785 


97248 


56537 


43463 


02752 


46215 


49 




12 


53819 


97243 


56576 


43424 


02757 


46181 


48 




13 


53854 


97238 


56615 


43385 


02762 


46146 


47 




14 


53888 


97234 


56654 


43346 


02766 


46112 


46 




15 


53922 


97229 


56693 


43307 


02771 


46078 


45 




16 


53957 


97224 


56732 


43268 


02776 


46043 


44 




17 


53991 


97220 


56771 


43229 


02780 


46009 


43 




18 


54025 


97215 


56810 


43190 


02785 


4597* 


42 




19 


54059 


97210 


56849 


43151 


02790 


45941 


41 
40 




20 


9.54093 


9.97206 


9.56887 


10.43113 


10.02794 


10.45907 




21 


54127 


97201 


56926 


43074 


02799 


45873 


39 




22 


54161 


97196 


56965 


43035 


02804 


45839 


38 




23 


54195 


97192 


57004 


42996 


02808 


45805 


37 




24 


54229 


97187 


57042 


42958 


02813 


45771 


36 




25 


54263 


97182 


57081 


42919 


02818 


45737 


35 




26 


54297 


97178 


57120 


42880 


02822 


45703 


34 




27 


54331 


97173 


57158 


42842 


02827 


45669 


33 




28 


54365 


97168 


57197 


42803 


02832 


45635 


32 




29 


54399 


97163 
9.97159 


57235 


42765 


02837 


45601 


31 




30 


9.54433 


9.57274 


10.42726 


10.02841 


10.45567 


30 




31 


54466 


97154 


57312 


42688 


02846 


45534 


29 




32 


54500 


97149 


57351 


42649 


02851 


45500 


28 




33 


54534 


97145 


57389 


42611 


02855 


45466 


27 




34 


54567 


97140 


57428 


42572 


02860 


45433 


26 




35 


54601 


97135 


57466 


42534 


02865 


45399 


25 




36 


54635 


97130 


57504 


42496 


02870 


45365 


24 




37 


54668 


97126 


57543 


42457 


02874 


45332 


23 




38 


54702 


97121 


57581 


42419 


02879 


45298 


22 




39 


54735 


97116 


57619 


42331 


02884 


45265 


21 




40 


9.54769 


9.97111 


9.57658 


10.42342 


10.02889 


10.45231 


20 




41 


54802 


97107 


57696 


42304 


02893 


45198 


19 




42 


54836 


97102 


57734 


42266 


02898 


45164 


18 




43 


54869 


97097 


57772 


42228 


02903 


45131 


17 




44 


54903 


97092 


57810 


42190 


02908 


45097 


16 




1 45 


54936 


97087 


57849 


42151 


02913 


45064 


15 




46 


54969 


97083 


57887 


42113 


02917 


45031 


14 




47 


55003 


97078 


57925 


42075 


02922 


44997 


13 




48 


55036 


97073 


57963 


42037 


02927 


44964 


12 




49 


55069 


97068 


58001 
9.58039 


41999 


02932 


44931 


11 




50 


9.55102 


9.97063 


10.41961 


10.02937 


10.44898 


10 




51 


55136 


97059 


58077 


41923 


02941 


44864 


9 




52 


55169 


97054 


58115 


41885 


02946 


44831 


8 




53 


55202 


97049 


58153 


41847 


02951 


44798 


7 




54 


55235 


97044 


58191 


41809 


02956 


44765 


6 




55 


55268 


97039 


58229 


41771 


02961 


44732 


5 




56 


55301 


97035 


58267 


41733 


02965 


44699 


4 




57 


55334 


97030 


58304 


41696 


02970 


44666 


3 




58 


55367 


97025 


58342 


41658 


02975 


44633 


2 




59 


55400 


97020 


58380 


41620 


02980 


44600 


1 




60 


55433 


97015 


58418 


41582 


02985 


44567 









Co-sine. 


Sine. 


Co- tang. 


Tangent. 


Co-secant 1 


Secant. 


M. 





69 Degrees. 



Artificial Sines, Tang, and Sec. 21 Degrees. 129 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 1 


Co-secant 







9.55433 


9.97015 


9.58418 


10.41582 


10.02985 


10.44567 


60 


1 


55466 


97010 


58455 


41545 


02990 


44534 


59 


2 


55499 


97005 


58493 


41507 


02995 


44501 


58 


3 


55532 


97001 


58531 


41469 


02999 


44468 


57 


4 


55564 


96996 


58569 


41431 


03004 


44436 


56 


5 


55597 


96991 


58606 


41394 


03009 


44403 


55 


6 


55630 


96986 


58644 


41356 


03014 


44370 


54 


7 


55663 


96981 


58681 


41319 


03019 


44337 


53 


8 


55695 


96976 


58719 


41281 


03024 


44305 


52 


9 


55728 


96971 


58757 


41243 


03029 


44272 


51 
50 


10 


9.55761 


9.96966 


9.58794 


10.41206 


10 03034 


10.44239 


11 


55793 


96962 


58832 


41168 


03038 


44207 


49 


12 


55826 


96957 


58869 


41131 


03043 


44174 


48 


13 


55858 


96952 


58907 


4109S 


03048 


44142 


47 


14 


55891 


96947 


58944 


41056 


03053 


44109 


46 


15 


55923 


96942 


58981 


41019 


03058 


44077 


45 


16 


55956 


96937 


59019 


40981 


03063 


44044 


44 


17 


55988 


96932 


59056 


40944 


03068 


44012 


43 


18 


56021 


96927 


59094 


40906 


03073 


43979 


42 


19 


56053 


96922 


59131 


40869 


03078 


43947 


41 
40 


20 


9.56085 


9.96917 


9.59168 


10.40832 


10.03083 


10.43915 


21 


56118 


96912 


59205 


40795 


03088 


43882 


39 


22 


56150 


96907 


59243 


40757 


03093 


43850 


38 


23 


56182 


96903 


59280 


40720 


03097 


43818 


37 


24 


56215 


96898 


59317 


40683 


03102 


43785 


36 


25 


56247 


96893 


59354 


40646 


03107 


43753 


35 


26 


56279 


96888 


59391 


40609 


03112 


43721 


34 


27 


56311 


96883 


59429 


40571 


03117 


43689 


33 


28 


56343 


96878 


59466 


40534 


03122 


43657 


32 


29 


56375 
9.56408 


96873 
9.96868 


59503 
9.59540 


40497 


03127 
10.03132 


43625 


31 


30 


10.40460 


10.43592 


30 


31 


56440 


96863 


59577 


40423 


03137 


43560 


29 


32 


56472 


96858 


59614 


40386 


03142 


43528 


28 


33 


56504 


96853 


59651 


40349 


03147 


43496 


27 


34 


56536 


96848 


59688 


40312 


03152 


43464 


26 


35 


56568 


, 96843 


59725 


40275 


03157 


43432 


25 


36 


56599 


96838 


59762 


40238 


03162 


43401 


24 


37 


56631 


96833 


59799 


40201 


03167 


43369 


23 


38 


56663 


96828 


59835 


40165 


03172 


43337 


22 


39 


56695 


96823 


59872 


40128 


03177 


43305 


21 
20 


40 


9.56727 


9.96818 


9.59909 


10.40091 


10.03182 


10.43273 


41 


56759 


96813 


59946 


40054 


03187 


43241 


19 


42 


56790 


96808 


59983 


40017 


03192 


43210 


18 


43 


56822 


96803 


60019 


39981 


03197 


43178 


17 


44 


56854 


96798 


60056 


39944 


03202 


43146 


16 


45 


56886 


96793 


60093 


39907 


03207 


43114 


15 


46 


56917 


96788 


60130 


39870 


03212 


43083 


14 


47 


56949 


96783 


60166 


39834 


03217 


43051 


13 . 


48 


56980 


96778 


60203 


39797 


03222 


43020 


12 


49 


57012 


96772 


60240 


39760 


03228 


42988 


11 


50 


9.57044 


9.96767 


9.60276 


10.39724 


10 03233 


10.42956 


10 


51 


57075 


96762 


60313 


39687 


03238 


42925 


9 


52 


57107 


96757 


60349 


39651 


03243 


42893 


8 


53 


57138 


96752 


60386 


39614 


03248 


42862 


7 


54 


57169 


96747 


60422 


39578 


03253 


47831 


6 


55 


57201 


96742 


60459 


39541 


03258 


J2799 


5 


56 


57232 


96737 


60495 


39505 


03263 


42768 


4 


57 


57264 


96732 


60532 


39468 


03268 


42736 


3 


58 


57295 


96727 


60568 


39432 


03273 


42705 


2 


59 


57326 


96722 


60605 


39395 


03278 


42674 


1 


60 


57358 


96717 


60641 


39359 


03283 


42642 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. | 




35 




68 D( 


jgrees 


3F 







30 Artificial Sines, Tang, and Sec. 22 Degrees. 



M^_ 


v Slne - 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 







^57358 


9.96717 


9.60641 


10.39359 


10 03233 


10.42642 


60 


1 ' 


^7389 


96711 


60677 


39323 


C6289 


42611 


59 


2 


57420 


96706 


60714 


39286 


03294 


42580 


58 


3 


57451 


96701 


60750 


39250 


03299 


42549 


57 


4 


57482 


9o696 


60786 


39214 


03304 


42518 


56 


5 


57514 


96691 


60823 


39177 


03309 


42486 


55 


6 


57545 


96686 


60859 


39141 


03314 


42455 


54 


7 


57576 


96681 


60895 


39105 


03319 


42424 


53 


8 


57607 


96676 


60931 


39069 


03324 


42393 


52 


9 


57638 


96670 


60967 


39033 


03330 


42362 


51 

50 


10 


9.57669 


9.96665 


9.61004 


10.38996 


10.03335 


10.42331 


11 


57700 


96660 


61040 


38960 


03340 


42300 


49 ; 


12 


57731 


96655 


61076 


38924 


03345 


42269 


48 


13 


57762 


96650 


61112 


38838 


03350 


42238 


47 


14 


57793 


96645 


61148 


38852 


03355 


42207 


46 


15 


57824 


96640 


61184 


38816 


03360 


42176 


45 


16 


57855 


96634 


61220 


38780 


03366 


42145 


44 


17 


57885 


96629 


61256 


38744 


03371 


42115 


43 


18 


57916 


96624 


61292 


38708 


03376 


42084 


42 


19 


57947 


96619 


61328 


33672 


03331 


42053 


41 


20 


9.57978 


9.96614 


9.61364 


10.38636 


10.03386 


10.42022 


40 


21 


58008 


96608 


61400 


38600 


03392 


41992 


39 


22 


58039 


96603 


61436 


38564 


03397 


41961 


38 


23 


58070 


96598 


61472 


38528 


03402 


41930 


37 


24 


58101 


96593 


61508 


38492 


03407 


41899 


36 


25 


58131 


96588 


61544 


38456 


03412 


41869 


35 


26 


58162 


96582 


61579 


38421 


03418 


41838 


34 


27 


58192 


96577 


61615 


38385 


03423 


41808 


33 


28 


58223 


96572 


61651 


38349 


03428 


41777 


32 


29 


58253 


96567 


61687 


38313 


03433 


41747 


— t 
30 


30 


9.58284 


9.96562 


9.61722 


10.38278 


10.03438 


10.41716 


31 


58314 


96556 


61758 


38242 


03444 


41686 


29 ' 


32 


58345 


96551 


61794 


38206 


03449 


41655 


28 


33 


58375 


96546 


61830 


38170 


03454 


41625 


27 ■ 


34 


58406 


96541 


61865 


38135 


03459 


41594 


26 


35 


58436 


96535 


61901 


38099 


03465 


41564 


25 


36 


58467 


96530 


61936 


38064 


03470 


41533 


24 


37 


58497 


96525 


61972 


38028 


03475 


41503 


23 


38 


58527 


96520 


62008 


37992 


03480 


41473 


22 


39 


58557 


96514 


62043 


37957 


03486 


41443 


21 


40 


9.58588 


9.96509 


9.62079 


10.37921 


10.03491 


10.41412 


20 


41 


58618 


96504 


62114 


37886 


03496 


41382 


19 


42 


58648 


96498 


62150 


37850 


03502 


41352 


18 


43 


58678 


96493 


62185 


37815 


03507 


41322 


17 


44 


58709 


96488 


62221 


37779 


03512 


41291 


16 


45 


58739 


96483 


62256 


37744 


03517 


41261 


15 


46 


58769 


96477 


62292 


37708 


03523 


41231 


14 


47 


58799 


96472 


62327 


37673 


03528 


41201 


13 


48 


58829 


96467 


62362 


37633 


03533 


41171 


12 


49 
50 


58859 
9.58889 


96461 
9.96456 


62398 


37602 


03539 


41141 


11 


9.62433 


10.37567 


10.03544 


10.41111 


10 


51 


58919 


96451 


62468 


37532 


03549 


41081 


9 ' 


52 


58949 


96445 


62504 


37496 


03555 


41051 


8 . 


53 


58979 


96440 


62539 


37461 


03560 


41021 


7 


54 


59009 


96435 


62574 


37426 


03565 


40991 


6 


55 


59039 


96429 


62609 


37391 


03571 


40961 


5 | 


56 


59069 


96424 


62645 


37355 


03576 


40931 


4 


57 


59098 


96419 


62680 


37320 


03581 


40902 


3 


58 


59128 


96413 


62715 


37285 


03587 


40872 


2 


59 


59158 


96408 


62750 


37250 


03592 


40842 


1 


60 


59188 


96403 


62785 


37215 


03597 


40812 





1 Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Recruit. 


M. 



67 Degrees. 





Artificial Sines, Tang. 


and Sec. 23 Degrees. 


131 


XVI. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 







9.59188 


9.96403 


9.62785 


10.37215 


10.03597 


10.40812 


60 


1 


59218 


96397 


62820 


37180 


03603 


40782 


59 


2 


59247 


96392 


32855 


37145 


03608 


40753 


58 


3 


59277 


96387 


62890 


37110 


03613 


40723 


57 


4 


59307 


96381 


62926 


37074 


03619 


40693 


56 


5 


59336 


96376 


62961 


37039 


03624 


40664 


55 


6 


59366 


96370 


62996 


37004 


03630 


40634 


54 


7 


59396 


96365 


63031 


36969 


03635 


40604 


53 


8 


59425 


96360 


63066 


36934 


03640 


40575 


52 


9 


59455 


96354 


63101 


36899 


03646 


40545 


51 


10 


9.59484 


9.96349 


9.63135 


10.36865 


10.03651 


10.40516 


50 


11 


59514 


96343 


63170 


36830 


03657 


40486 


49 


12 


59543 


96338 


63205 


36795 


03662 


40457 


48 


13 


59573 


96333 


63240 


36760 


03667 


40427 


47 


14 


59602 


96327 


63275 


36725 


03673 


40398 


46 


15 


59632 


96322 


63310 


36690 


03678 


40368 


45 


16 


59661 


96316 


63345 


36655 


03684 


40339 


44 


17 


59690 


96311 


63379 


36621 


03689 


40310 


43 


18 


59720 


96305 


63414 


36586 


03695 


40280 


42 


19 


59749 


96300 


63449 


36551 


03700 
10.03706 


40251 
10.40222 


41 

40 


20 


9.59778 


9.96294 


9.63484 


10.36516 


21 


59808 


96289 


63519 


36481 


03711 


40192 


39 


22 


59837 


96284 


63553 


36447 


03716 


40163 


38 


23 


59866 


96278 


63588 


36412 


03722 


40134 


37 


24 


59895 


96273 


63623 


36377 


03727 


40105 


36 


25 


59924 


96267 


63657 


36343' 


03733 


40076 


35 


26 


59954 


96262 


63692 


36308 


03738 


40046 


34 


■ 27 


59983 


96256 


63726 


36274 


03744 


40017 


33 


28 


60012 


96251 


63761 


36239 


03749 


39988 


32 


29 
30 


60041 
9.60070 


96245 
9.96240 


63796 
9.63830 


36204 


03755 


39959 


31 


10.36170 


10.03760 


10.39930 


30 


31 


60099 


96234 


63865 


36135 


03766 


39901 


29 


32 


60128 


96229 


63899 


36101 


03771 


39872 


28 


33 


60157 


96223 


63934 


36066 


03777 


39843 


27 


34 


60186 


96218 


63968 


36032 


03782 


39814 


26 


35 


60215 


96212 


64003 


35997 


03788 


39785 


25 


36 


60244 


96207 


64037 


35963 


03793 


39756 


24 


37 


60273 


96201 


64072 


35928 


03799 


39727 


23 


38 


60302 


96196 


64106 


35894 


03804 


39698 


22 


39 


60331 


96190 


64140 

9.64175 


35860 


03810 


39669 


21 
20 


40 


9.60359 


9.96185 


10.35825 


10.03815 


10.39641 


41 


60388 


96179 


64209 


35791 


03821 


39612 


19 


42 


60417 


96174 


64243 


35757 


03826 


39583 


18 


43 


60446 


96168 


64278 


35722 


03832 


39554 


17 


44 


60474 


96162 


64312 


35688 


03838 


39526 


16 


45 


60503 


96157 


64346 


35654 


03843 


39497 


15 


46 


60532 


96151 


64381 


35619 


03849 


39468 


14 


47 


60561 


96146 


64415 


35585 


03854 


39439 


13 


48 


60589 


96140 


64449 


35551 


03860 


39411 


12 


49 


60618 


96135 


64483 


35517 


03865 


39382 


11 
10 


50 


9.60646 


9.96129 


9.64517 


10.35483 


10.03871 


10.39354 


51 


60675 


96123 


64552 


35448 


03877 


39325 


9 


52 


60704 


96118 


64586 


35414 


03882 


39296 


8 


53 


60732 


96112 


64620 


35380 


03888 


39268 


7 


54 


60761 


96107 


64654 


35346 


03893 


39239 


6 , 


55 


60789 


96101 


64688 


35312 


03899 


39211 


5 


56 


60818 


96095 


64722 


35278 


03905 


39182 


4 


57 


60846 


96090 


64756 


35244 


03910 


39154 


3 


58 


60875 


96084 


64790 


35210 


03916 


39125 


2 


59 


60903 


96079 


64824 


35176 


03921 


39097 


1 


60 


60931 


96073 


64858 


35142 


03927 


39069 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 



66 Degrees. 



1 32 Artificial Sines, Tang, and Sec. 24 Degrees. 



M. 


Sine. 


Co-sine. 
9.96073 


Tangent. 


Co-tang. 
10.35142 


Secant. 


Co-secant 


60 




9.60931 


9.64858 


10.03927 


10.39069 




1 


60960 


96067 


64892 


35108 


03933 


39040 


59 




2 


60988 


96062 


64926 


35074 


03938 


39012 


58 




3 


61016 


96056 


64960 


35040 


03944 


38984 


57 




4 


61045 


96050 


64994 


35006 


03950 


38955 


56 




5 


61073 


96045 


65028 


34972 


03955 


38927 


55 




6 


61101 


96039 


65062 


34938 


03961 


38899 


54 




7 


61129 


96034 


65096 


34904 


03966 


38871 


53 




8 


61158 


96028 


65130 


34870 


03972 


38842 


52 




9 


61186 


96022 


65164 


34836 


03978 


38814 


51 




10 


9.61214 


9.96017 


9.65197 


10.34803 


10.03983 


10.38786 


~50~ 




11 


61242 


96011 


65231 


34769 


03989 


38758 


49 




12 


61270 


96005 


65265 


34735 


03995 


38730 


48 




13 


61298 


96000 


65299 


34701 


04000 


38702 


47 




14 


61326 


95994 


65333 


34667 


04006 


38674 


46 




15 


61354 


95988 


65366 


34634 


04012 


38646 


45 




16 


61382 


95982 


65400 


34600 


04018 


38618 


44 




17 


61411 


95977 


65434 


34566 


04023 


38589 


43 




18 


61438 


95971 


65467 


34533 


04029 


38562 


42 




19 


61466 


95965 


65501 


34499 


04035 


38534 


41 




20 


9.61494 


9.95960 


9.65535 


10.34465 


"10.04040 


10.38506 


40 




21 


61522 


95954 


65568 


34432 


04046 


38478 


39 




22 


61550 


95948 


65602 


34398 


04052 


38450 


38 




23 


61578 


95942 


65636 


34364 


04058 


38422 


37 




24 


61606 


95937 


65669 


34331 


04063 


38394 


36 




25 


61634 


95931 


65703 


34297 


04069 


38366 


35 




26 


61662 


95925 


65736 


34264 


04075 


38338 


34 




27 


61689 


95920 


65770 


34230 


04080 


38311 


33 




28 


61717 


95914 


65803 


34197 


04086 


38283 


32 




29 


61745 


95908 


65837 


34163 


04092 


38255 


31 




30 


9.61773 


9.95902 


9.65S70 


10.34130 


10.04098" 


10.38227" 


~3(F 




31 


61800 


95897 


65904 


34096 


04103 


38200 


29 




32 


61828 


95891 


65937 


34063 


04109 


38172 


28 




33 


61856 


95885 


65971 


34029 


04115 


38144 


27 




34 


61883 


95879 


66004 


33996 


04121 


38117 


26 




35 


61911 


95873 


66038 


33962 


04127 


38039 


25 




36 


61939 


95868 


66071 


33929 


04132 


38061 


24 




37 


61966 


95862 


66104 


33896 


04138 


38034 


23 




38 


61994 


95856 


66138 


33862 


04144 


38006 


22 




39 


62021 


95850 


66171 


33829 


04150 


37979 


21 




40 


9.62049 


9.95844 


9.66204 


10.33796 


10.04156 


10.37951 


20 




41 


62076 


95839 


66238 


33762 


04161 


37924 


19 




42 


62104 


95833 


66271 


33729 


04167 


37896 


18 




43 


62131 


95827 


66304 


33696 


04173 


37869 


17 




44 


62159 


95821 


66337 


33663 


04179 


37841 


16 




45 


62186 


95815 


66371 


33629 


04185 


37814 


15 




46 


62214 


95810 


66404 


33596 


04190 


37786 


14 




47 


62241 


95804 


66437 


33563 


04196 


37759 


13 




48 


62268 


95798 


66470 


33530 


04202 


37732 


12 




49 


62296 


95792 


66503 
9.66537 


33497 


04208 


37704 
10.37677 


11 
10 




50 


9.62323 


9.95786 


10.33463 


10.04214 




51 


62350 


95780 


66570 


33430 


04220 


37650 


9 




52 


62377 


95775 


66603 


33397 


04225 


37623 


8 




53 


62405 


95769 


66636 


33364 


04231 


37595 


7 




54 


62432 


95763 


66669 


33331 


04237 


37568 


6 




55 


62459 


95757 


66702 


33298 


04243 


37541 


5 




56 


62486 


95751 


66735 


33265 


04249 


37514 


«* 




57 


62513 


95745 


66768 


33232 


04255 


37487 


3 




58 


62541 


95739 


66801 


33199 


04261 


37459 


2 




50 


62568 


95733 


66834 


33166 


04267 


37432 


1 




e'o 


62595 


95728 

Pine. 


66867 


33133 


04272 


37405 







<"o-(an?. 


Tangent. 


Co-secant 


Secant. 1 





05 Decrees. 



Artificial Sines, Tang, and Sec. 25 Degrees. 133 



LSI. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 







9.62595 


9.95728 


9.66867 


10.33133 


10.04272 


10.37405 


60 


1 


62622 


95722 


66900 


33100 


04278 


37378 


59 


2 


62649 


95716 


66933 


33067 


04284 


37351 


58 


3 


62676 


95710 


66966 


33034 


04290 


37324 


57 


4 


62703 


95704 


66999 


33001 


04296 


37297 


56 


5 


62730 


95698 


67032 


32968 


04302 


37270 


55 


6 


62757 


95692 


67065 


32935 


04308 


37243 


54 


7 


62784 


95686 


67098 


32902 


04314 


37216 


53 


8 


62811 


95680 


67131 


32869 


04320 


37189 


52 


9 
W 


62838 


95674 


67163 


32837 


04326 


37162 


51 


9.62865 


9.95668 


9.67196 


10.32804 


10.04332 


10.37135 


50 


11 


62892 


95663 


67229 


32771 


04337 


37108 


49 


12 


62918 


95657 


67262 


32738 


04343 


37082 


48 


13 


62945 


95651 


67295 


32705 


04349 


37055 


47 


14 


62972 


95645 


67327 


32673 


04355 


37028 


46 


15 


62999 


95639 


67360 


32640 


04361 


37001 


45 


16 


63026 


95633 


67393 


32607 


04367 


36974 


44 


17 


63052 


95627 


67426 


32574 


04373 


36948 


43 


18 


63079 


95621 


67458 


32542 


04379 


36921 


42 


19 


63106 


95615 


67491 


32509 


04385 


36894 


41 


20 


9.63133 


9.95609 


9.67524 


10.32476 


10.04391 


10.36867 


40 


21 


63159 


95603 


67556 


32444 


04397 


36841 


39 


22 


63186 


95597 


67589 


32411 


04403 


36814 


38 


23 


63213 


95591 


67622 


32378 


04409 


36787 


37 


24 


63239 


95585 


67654 


32346 


04415 


36761 


36 


25 


63266 


95579 


67687 


32313 


04421 


36734 


3', 


26 


63292 


95573 


67719 


32281 


04427 


36708 


34 


27 


63319 


95567 


67752 


32248 


04433 


36681 


33 


28 


63345 


95561 


67785 


32215 


04439 


36655 


32 


29 
30 


63372 


95555 


67817 


32183 


04445 


36628 


31 


9.63398 


9.95549 


9.67850 


10.32150 


10.04451 


10.36602 


30 


31 


63425 


95543 


67882 


32118 


04457 


36575 


29 


32 


63451 


95537 


67915 


32085 


04463 


36549 


28 


33 


63478 


95531 


67947 


32053 


04469 


36522 


27 


34 


63504 


95525 


67980 


32020 


04475 


36496 


26 


35 


63531 


95519 


68012 


31988 


04481 


36469 


25 


36 


63557 


95513 


68044 


31956 


04487 


36443 


24 


37 


63583 


95507 


68077 


31923 


04493 


36417 


23 


38 


63610 


95500 


68109 


31891 


04500 


36390 


22 


39 


63636 


95494 


63142 


31858 


04506 


36364 


21 


40 


9.63662 


9.95488 


9.68174 


10.31826 


10.04512 


10.36338 


20 


41 


63689 


95482 


68206 


31794 


04518 


36311 


19 


42 


63715 


95476 


68239 


31761 


04524 


36285 


18 


43 


63741 


95470 


68271 


31729 


04530 


36259 


17 


44 


63767 


95464 


68303 


31697 


04536 


36233 


16 


45 


63794 


95458 


68336 


31664 


04542 


36206 


15 


46 


63820 


95452 


68368 


31632 


04548 


36180 


14 


47 


63846 


95446 


68400 


31600 


04554 


36154 


13 


48 


63872 


95440 


68432 


31568 


04560 


36128 


12 


49 


63898 


95434 
9.95427 


68465 


31535 


04566 


36102 


11 


50 


9.63924 


9.68497 


10.31503 


10.04573 


10.36076 


10 


51 


63950 


95421 


68529 


31471 


04579 


36050 


9 


52 


63976 


95415 


63561 


31439 


04585 


36024 


8 


53 


64002 


95409 


68593 


31407 


04591 


35998 


7 


54 


64028 


95403 


68626 


31374 


04597 


35972 


6 


55 


64054 


95397 


68658 


31342 


04603 


35946 


5 


56 


64080 


95391 


68690 


31310 


04609 


35920 


4 


57 


64106 


95384 


68722 


31278 


04616 


35894 


3 


58 


64132 


95378 


68754 


31246 


04622 


35868 


2 


59 


64158 


95372 


68786 


31214 


04628 


35842 


1 


60 


64184 
.Cq-rsineT 


95366 


68818 


31182 


04634 


35816 



M. 


Sine. 


Co-tan^. 


Tansent. 


Co-secant 


Secant. 



35 



64 Degrees. 



134 Artificial Sines, Tang, and Sec. 26 Degrees. 



M. 


Sme. 


Co-sine. 


Tangent. 
9.68818 


Co-tang. 


Secant. 


Co-secant 


60 







9.64184 


9.95366 


10.31182 


10.04634 


10.35816 




1 


64210 


95360 


68850 


31150 


04640 


35790 


59 




2 


64236 


95354 


68882 


31118 


04646 


35764 


58 




3 


64262 


95348 


68914 


31086 


04652 


35738 


57 




4 


64288 


95341 


68946 


31054 


04659 


35712 


56 




5 


64313 


95335 


68978 


31022 


04665 


35687 


55 




6 


64339 


95329 


69010 


30990 


04671 


35661 


54 




7 


64365 


95323 


69042 


30958 


04677 


35635 


53 




8 


64391 


95317 


69074 


30926 


04683 


35609 


52 




9 


64417 


95310 


69106 


30894 


04690 


35583 


51 




10 


9.64442 


9.95304 


9.69138 


10.30862 


10.04696 


10.35558 


50 




11 


64468 


95298 


69170 


30830 


04702 


35532 


49 




12 


64494 


95292 


69202 


30798 


04708 


35506 


48 




13 


64519 


95286 


69234 


30766 


04714 


35481 


47 




14 


64545 


95279 


69266 


30734 


04721 


35455 


46 




15 


64571 


95273 


69298 


30702 


04727 


35429 


45 




16 


64596 


95267 


69329 


30671 


04733 


35404 


44 




17 


64622 


95261 


69361 


30639 


04739 


35378 


43 




18 


64647 


95254 


69393 


30607 


04746 


35353 


42 




19 


64673 


95248 


69425 


30575 


04752 


35327 


41 




20 


9.64698 


9.95242 


9.69457 


10.30543 


10.04758 


10.35302 


40 




21 


64724 


95236 


69488 


30512 


04764 


35276 


39 




22 


64749 


95229 


69520 


30480 


04771 


35251 


38 




23 


64775 


95223 


69552 


30448 


04777 


35225 


37 




24 


64800 


95217 


69584 


30416 


04783 


35200 


36 




25 


64826 


95211 


69615 


30385 


04789 


35174 


35 




26 


64851 


95204 


69647 


30353 


04796 


35149 


34 




27 


64877 


95198 


69679 


30321 


04802 


35123 


33 




28 


64902 


95192 


69710 


30290 


04808 


35098 


32 




29 


64927 


95185 


69742 


30258 


04815 


35073 


31 
30 




30 


9.64953 


9.95179 


9.69774 


10.30226 


10.04821 


10.35047 




31 


64973 


95173 


69805 


30195 


04827 


35022 


29 




32 


65003 


95167 


69837 


30163 


04833 


34997 


28 




33 


65029 


95160 


69868 


30132 


04840 


34971 


27 




34 


65054 


95154 


69900 


30100 


04846 


34946 


26 




35 


65079 


95148 


69932 


30068 


04852 


34921 


25 




36 


65104 


95141 


69963 


30037 


04859 


34896 


24 




37 


65130 


95135 


69995 


30005 


04865 


34870 


23 




33 


65155 


95129 


70026 


29974 


04871 


34845 


22 




39 


65 180 


95122 


70058 


29942 


04878 


34820 


21 




40 


9.65205 


9.95116 


9.70089 


10.29911 


10.04884 


10.34795 


20 




41 


65230 


95110 


70121 


29879 


04890 


34770 


19 




42 


65255 


95103 


70152 


29848 


04897 


34745 


18 




43 


65281 


95097 


70184 


29816 


04903 


34719 


17 




44 


65306 


95090 


70215 


29785 


04910 


34694 


16 




45 


65331 


95084 


70247 


29753 


04916 


34669 


15 




46 


65356 


95078 


70278 


29722 


04922 


34644 


14 




47 


65381 


95071 


70309 


29691 


04929 


34619 


13 




48 


65406 


95065 


70341 


29659 


04935 


34594 


12 




49 


65431 


95059 


70372 


29628 


04941 


34569 


11 




50 


9.65456 


9.95052 


9.70404 


10.29596 


10.04948 


10.34544 


10 




51 


65481 


95046 


70435 


29565 


04954 


34519 


9 




52 


65506 


95039 


70466 


29534 


04961 


34494 


8 




53 


6553 


95033 


70498 


29502 


04967 


34469 


7 




54 


6555*. 


95027 


70529 


29471 


04973 


34444 


6 




55 


6558C 


95020 


70560 


29440 


04980 


34420 


5 




56 


65605 


95014 


70592 


29408 


04986 


34395 


4 




57 


65630 


95007 


70623 


29377 


04993 


34370 


3 




58 


65655 


95001 


70654 


29346 


04999 


34345 


2 




59 


65680 


94995 


70685 


29315 


05005 


34320 


1 




60 


65705 


94988 


70717 


29283 


05012 


34295 









Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. | M. 





63 Degrees. 



Artificial Sines, Tang, and Sec. 27 Degrees. 135 



M. 


-Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 
10.05012 


Co-secant 
10.34295 


60 





9.65705 


9.94988 


9.70717 


10.29283 


1 


65729 


94982 


70748 


29252 


05018 


34271 


59 


2 


65754 


94975 


70779 


29221 


05025 


34246 


58 


3 


65779 


94969 


70810 


29190 


05031 


34221 


57 


4 


65804 


94962 


70841 


29159 


05038 


34196 


56 


5 


65828 


94956 


70873 


29127 


05044 


34172 


55 


6 


65853 


94949 


70904 


29096 


05051 


34147 


54 


7 


65878 


94943 


70935 


29065 


05057 


34122 


53 


8 


65902 


94936 


70966 


29034 


05064 


34098 


52 


9 


65927 
9.65952 


94930 


70997 


29003 


05070 


34073 
10.34048 


51 

50 


10 


9.94923 


9.71028 


10.28972 


10.05077 


11 


65976 


94917 


71059 


28941 


05083 


34024 


49 


12 


C6001 


94911 


71090 


28910 


05089 


33999 


43 


13 


66025 


94904 


71121 


28879 


05096 


33975 


47 


14 


66050 


94898 


71153 


28847 


05102 


33950 


46 


15 


66075 


94891 


71184 


28816 


05109 


33925 


45 


16 


66099 


94885 


71215 


28785 


05115 


33901 


44 


17 


66124 


94878 


71246 


28754 


05122 


33876 


43 


18 


66148 


94871 


71277 


28723 


05129 


33852 


42 


19 


66173 


94865 


71308 


28692 


05135 


33827 


41 


20 


9.66197 


9.94858 


9.71339 


10.28661 


10.05142 


10.33803 


40" 


21 


66221 


94852 


71370 


28630 


05148 


33779 


39 


22 


66246 


94845 


71401 


28599 


05155 


33754 


38 


23 


66270 


94839 


71431 


28569 


05161 


33730 


37 


24 


66295 


94832 


71462 


28538 


05168 


33705 


36 


25 


66319 


94826 


71493 


28507 


05174 


33681 


35 


26 


66343 


94819 


71524 


28476 


05181 


33657 


34 


27 


66368 


94813 


71555 


28445 


05187 


33632 


33 


28 


66392 


94806 


71586 


28414 


05194 


22808 


32 


29 


66416 


94799 


71617 


28383 


05201 


33584 


31 


30 


9.66441 


9.94793 


9.71648 


10.28352 


10.05207 


10.33559 


30 


31 


66465 


94786 


71679 


28321 


05214 


33535 


29 


32 


66489 


94780 


71709 


28291 


05220 


33511 


28 


33 


66513 


94773 


71740 


28260 


05227 


33487 


27 


34 


66537 


94767 


71771 


28229 


05233 


33463 


26 


35 


66562 


94760 


71802 


28198 


05240 


33438 


25 


36 


66586 


94753 


71833 


28167 


05247 


33414 


24 


37 


66610 


94747 


71863 


28137 


05253 


33390 


23 


38 


66634 


94740 


71894 


28106 


05260 


33366 


22 


39 


66658 
9.66682 


94734 


71925 


28075 


05266 


33342 


21 
20 


40 


9.94727 


9.71955 


10.28045 


10.05273 


10.33318 


41 


66706 


94720 


71986 


28014 


05280 


33294 


19 


42 


66731 


94714 


72017 


27983 


05286 


33269 


18 


43 


66755 


94707 


72048 


27952 


05293 


33245 


17 


44 


66779 


94700 


72078 


27922 


05300 


33221 


16 


45 


66803 


94694 


72109 


27891 


05306 


33197 


15 


46 


66827 


94687 


72140 


27860 


05313 


33173 


14 


47 


66851 


94680 


72170 


27830 


05320 


33149 


13 


48 


66875 


94674 


72201 


27799 


05326 


33125 


12 


49 


66899 
9.66922 


94667 
9.94660 


72231 


27769 


05333 
10.05340 


33101 
10.33078 


11 
10 


50 


9.72262 


10.27738 


1 51 


66946 


94654 


72293 


27707 


05346 


33054 


9 


52 


66970 


94647 


72323 


27677 


05353 


33030 


8 


53 


66994 


94640 


72354 


27646 


05360 


33006 


7 


54 


67018 


94634 


72384 


27616 


05366 


32982 


6 


55 


67042 


94627 


72415 


27585 


05373 


32958 


5 


56 


67066 


94620 


72445 


27555 


05380 


32934 


4 


57 


67090 


94614 


72476 


27524 


05386 


32910 


3 


58 


67113 


94607 


72506 


27494 


05393 


32887 


2 


59 


67137 


94600 


72537 


27463 


05400 


32863 


1 


60 


67161 


94593 


72567 


27433 


05407 


32839 
Secant. 




M. 




Co-sine. 


Sine. 


Co- tang. 


Tangent. 


Co-secant 



62 Degrees. 



136 Artificial Sines, Tang, and Sec. 28 Degrees. 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 







9.671CT1 


9.94593 


9.72567 


10.2743:3 


10.05407 


10.32839 


60 


1 


67185 


94587 


72598 


27402 


05413 


32815 


59 


2 


67208 


94580 


72628 


27372 


05420 


32792 


58 


3 


67232 


94573 


72659 


27341 


05427 


32768 


57 


4 


67256 


94567 


72689 


27311 


05433 


327-44 


56 


5 


67280 


94560 


72720 


27280 


05440 


32720 


55 


6 


67303 


94553 


72750 


27250 


05447 


32697 


54 


7 


67327 


94546 


72780 


27220 


05454 


32673 


53 


8 


67350 


94540 


72811 


27189 


05460 


32650 


52 


9 


67374 


94533 


72841 


27159 


05467 


32626 


51 


10 


9.67398 


9.94526 


9.72872 


10.27128 


10.05474 


' 10.32602 


50 


11 


67421 


94519 


72902 


27098 


05481 


32579 


49 


12 


67445 


94513 


72932 


27068 


05487 


32555 


48 


13 


67468 


94506 


72963 


27037 


05494 


32532 


47 


14 


67492 


94499 


72993 


27007 


05501 


32508 


46 


15 


67515 


94492 


73023 


26977 


05508 


32485 


45 


16 


67539 


94485 


73054 


26946 


05515 


32461 


44 


17 


67562 


94479 


73084 


26916 


05521 


32438 


43 


18 


67586 


94472 


73114 


26886 


05528 


32414 


42 


19 


67609 


94465 


73144 


26856 


05535 


32391 


41 


20 


9.67633 


9.94458 


9.73175 


~10T26825 


10.05542 


10.32367 


40 


21 


67656 


94451 


73205 


26795 


05549 


32344 


39 


22 


67680 


94445 


73235 


26765 


05555 


32320 


38 


23 


67703 


94438 


73265 


26735 


05562 


32297 


37 


24 


67726 


94431 


73295 


26705 


05569 


32274 


36 


25 


67750 


94424 


73326 


26674 


05576 


32250 


35 


26 


67773 


94417 


73356 


26644 


05583 


32227 


34 


27 


67796 


94410 


73386 


26614 


05590 


32204 


33 


28 


67820 


94404 


73416 


26584 


05596 


32180 


32 


29 


67843 


94397 


73446 


26554 


05603 


32157 


31 


30 


9.67866 


9.94390 


9.73476 


10.26524 


10.05610 


10.32134 


30 


31 


67890 


94383 


73507 


26493 


05617 


32110 


29 


32 


67913 


94376 


73537 


26463 


05624 


32087 


28 


33 


67936 


94369 


73567 


26433 


05631 


32064 


27 


34 


67959 


94362 


73597 


26403 


05638 


32041 


26 


35 


67982 


94355 


73627 


26373 


05645 


32018 


25 


36 


68006 


94349 


73657 


26343 


05651 


31994 


24 


37 


68029 


94342 


73687 


26313 


05658 


31971 


23 


38 


68052 


94335 


73717 


26283 


05665 


31948 


22 


39 


68075 


94328 


73747 


26253 


05672 


31925 


21 


40 


9.68098 


9.94321 


9.73777 


10.26223 


10.05679 


10.31902 


20 


41 


68121 


94314 


73807 


26193 


05686 


31379 


19 


42 


68144 


94307 


73837 


26163 


05693 


31856 


18 


43 


68167 


94300 


73867 


26133 


05700 


31833 


17 


44 


68190 


94293 


73897 


26103 


05707 


31810 


16 


45 


68213 


94286 


73927 


26073 


05714 


31787 


15 


46 


68237 


94279 


73957 


26043 


05721 


31763 


14 


47 


68260 


94273 


73987 


26013 


05727 


31740 


13 


48 


68283 


94266 


74017 


25983 


05734 


31717 


12 


49 
~50~ 


68305 
9.68328 


94259 


74047 


25953 
10.25923 


05741 
10.05748 


31695 
10.31672 


11 
10 


9.94252 


9.74077 


51 


68351 


94245 


74107 


25893 


05755 


31649 


9 


52 


68374 


94238 


74137 


25863 


05762 


31626 


8 


53 


68397 


94231 


74166 


25834 


05769 


31603 


7 


54 


68420 


94224 


74196 


25804 


05776 


31580 


6 


55 


68443 


94217 


74226 


25774 


05783 


31557 


5 


56 


68466 


94210 


74256 


25744 


05790 


31534 


4 


57 


68489 


94203 


74286 


25714 


05797 


31511 


3 


58 


68512 


94196 


74316 


25684 


05804 


31488 


2 


59 


68534 


94189 


74345 


25655 


0581 1 


31466 


1 


60 


68557 


94182 


74375 


25625 
Tangent. 


05818 


31443 




M. 


1 Co-sine. 


Sine. 


Co-tang. 


Co-secant 


Srcant. 



61 Degrees. 



Artificial Sines, Tang, and Sec. 29 Degrees. 13' 



M. 


Sine. 


Co-sine. 
9.94182 


Tangent. 


Co-tang. 


Secant. 


Co-secant 







9.68557 


9.74375 


10.25625 


10.05818 


10.31443 


60 


1 


68580 


94175 


74405 


25595 


05825 


31420 


59 


2 


68603 


94168 


74435 


25565 


05832 


31397 


58 


3 


68625 


94161 


74465 


25535 


05839 


31375 


57 


4 


68648 


94154 


74494 


25506 


05846 


31352 


56 


5 


68671 


94147 


74524 


25476 


05853 


31329 


55 


6 


68694 


94140 


74554 


25446 


05860 


31306 


54 


7 


68716 


94133 


74583 


25417 


05867 


31284 


53 


8 


68739 


94126 


74613 


25387 


05874 


31261 


52 


9 


68762 


94119 


74643 


25357 


05881 


31238 


51 

50 


10 


9.68784 


9.94112 


9.74673 


10.25327 


10.05888 


10.31216 


11 


68807 


. 94105 


74702 


25298 


05895 


31193 


49 


12 


68829 


94098 


74732 


25268 


05902 


31171 


48 


13 


68852 


94090 


74762 


25238 


05910 


31148 


47 


14 


68875 


94083 


74791 


25209 


05917 


31125 


46 


15 


68897 


94076 


74821 


25179 


05924 


31103 


45 


16 


68920 


94069 


74851 


25149 


05931 


31080 


44 


17 


68942 


94062 


74880 


25120 


05938 


31058 


43 


18 


68965 


94055 


74910 


25090 


05945 


31035 


42 


19 


68987 


94048 
9.94041 


74939 


25061 


05952 


31013 
10.30990 


41 
40 


20 


9.69010 


9.74969 


10.25031 


10.05959 


21 


69032 


94034 


74998 


25002 


05966 


30968 


39 


ncy 


69055 


94027 


75028 


24972 


05973 


30945 


38 


23 


69077 


94020 


75058 


24942 


05980 


30923 


37" 


24 


69100 


94012 


75087 


24913 


05988 


30900 


36 


25 


69122 


94005 


75117 


24883 


05995 


30878 


35 


26 


69144 


93998 


75146 


24854 


06002 


30856 


34 


27 


69167 


93991 


75176 


24824 


06009 


30833 


33 


28 


69189 


93984 


75205 


24795 


06016 


30811 


32 


29 


69212 


93977 


75235 


24765 


06023 


30788 


31 


30 


9.69234 


9.93970 


9.75264 


10.24736 


10.06030 


10.30766 


30 


31 


69256 


93963 


75294 


24706 


06037 


30744 


29 


32 


69279 


93955 


75323 


24677 


06045 


30721 


28 


33 


69301 


93948 


75353 


24647 


06052 


30699 


27 


34 


69323 


93941 


75382 


24618 


06059 


30677 


26 


35 


69345 


93934 


75411 


24589 


06066 


30655 


25 


36 


69368 


93927 


75441 


24559 


06073 


30632 


24 


1 37 


69390 


93920 


75470 


24530 


06080 


30610 


23 


38 


69412 


93912 


75500 


24500 


06088 


30588 


22 


39 


69434 


93905 


75529 


24471 


06095 


30566 
10.30544 


21 
20 


40 


9.69456 


9.93898 


9.75558 


10.24442 


10.06102 


41 


69479 


93891 


75588 


24412 


06109 


30521 


19 


42 


69501 


93884 


75617 


24383 


06116 


30499 


18 


| 43 


69523 


93876 


75647 


24353 


06124 


30477 


17 


1 44 


69545 


93869 


75676 


24324 


06131 


30455 


16 


1 45 


69567 


93862 


75705 


24295 


06138 


30433 


15 


46 


69589 


93855 


75735 


24265 


06145 


30411 


14 


47 


69611 


93847 


75764 


24236 


06153 


30389 


13 


48 


69633 


93640 


75793 


24207 


06160 


30367 


12 


49 


69655 


93833 


75822 


24178 


06167 


30345 


11 


50 


9.69677 


9.93826 


9.75852 


10.24148 


10.06174 


10.30323 


10 


51 


69699 


93819 


75881 


24119 


06181 


30301 


9 


52 


69721 


93811 


75910 


24090 


06189 


30279 


8 


53 


69743 


93804 


75939 


24061 


06196 


30257 


7 


54 


69765 


93797 


75969 


24031 


06203 


30235 


6 


55 


69787 


93789 


75998 


24002 


06211 


30213 


5 


56 


69809 


93782 


76027 


23973 


06218 


30191 


4 


57 


69831 


93775 


76056 


23944 


06225 


30169 


3 


58 


69853 


93768 


76086 


23914 


06232 


30147 


2 


59 


69875 


93760 


76115 


23885 


06240 


30125 


1 


60 


69897 


93753 


76144 


23856 


06247 


30103 


© 




Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant 


M. 



60 Degrees. 3 & 



138 Artificial Sines, Tang, and Sec. 30 Defjreeo. 



M. 


Sine. 


Co-sine. 
9.93753 


Tangent. 

9.76144 


Co-tang. 


Secant. 


Co -secant 




0» 


9.69897 


10.23856 


10.06247 


1* 30103 


60 


1 


69919 


93746 


76173 


23827 


06254 


30081 1 59 


2 


69941 


93738 


76202 


23798 


06262 


30059 1 58 


3 


69963 


93731 


76231 


23769 


06269 


30037 


57 


4 


69984 


93724 


76261 


23739 


06276 


30016 


56 


5 


70006 


93717 


76290 


23710 


06283 


29994 


55 


6 


70028 


93709 


76319 


23681 


06291 


29972 


54 


7 


70050 


93702 


76348 


23652 


06298 


29950 


53 


8 


70072 


93695 


76377 


23623 


06305 


29928 


52 


9 


70093 


93687 


76406 


23594 


06313 


29907 
If 29885 


51 


10 


9.70115 


9.93680 


9.76435 


10.23565 


10.06320 


50 


11 


70137 


93673 


76464 


23536 


06327. 


29863 


49 


12 


70159 


93665 


76493 


23507 


06335 


29841 


48 


13 


70180 


93658 


76522 


23478 


06342 


29820 


47 


14 


70202 


93650 


76551 


23449 


06350 


29798 


46 


15 


70224 


93643 


76580 


23420 


06357 


29776 


45 


16 


70245 


93636 


76609 


23391 


06364 


29755 


44 


17 


70267 


93628 


76639 


23361 


06372 


29733 


43 


18 


70288 


93621 


76668 


23332 


06379 


29712 


42 


19 


70310 


93614 


76697 


23303 


06386 


29690 


41 


20 


9.70332 


9.93606 


9.76725 


10.23275 


10.06394 


V 29668 


40 


21 


70353 


93599 


76754 


23246 


06401 


29647 


39 


22 


70375 


93591 


76783 


23217 


06409 


29625 


38 


23 


70396 


93584 


76812 


23188 


06416 


29604 


37 


24 


70418 


93577 


76841 


23159 


06423 


29582 


36 


25 


70439 


93569 


76870 


23130 


06431 


29561 


35 


26 


70461 


93562 


76899 


23101 


06438 


29539 


34 


27 


70482 


93554 


76928 


23072 


06446 


29518 


33 


28 


70504 


93547 


76957 


23043 


06453 


29496 


32 


29 


70525 


93539 


76986 
9.77015 


23014 


06461 


29475 
1C 29453 


31 
30 


30 


9.70547 


9.93532 


10.22985 


10.06468 


31 


70568 


93525 


77044 


22956 


06475 


29432 


29 


32 


70590 


93517 


77073 


22927 


06483 


29410 


28 


33 


70611 


93510 


77101 


22899 


06490 


29389 


27 


34 


70633 


93502 


77130 


22870 


06498 


29367 


26 


35 


70654 


93495 


77159 


22841 


06505 


29346 


25 


36 


70675 


93487 


77188 


22812 


06513 


29325 


24 


37 


70697 


93480 


77217 


22783 


06520 


29303 


23 


38 


70718 


93472 


77246 


22754 


06528 


29282 


22 


39 


70739 


93465 


77274 


22726 


06535 


29261 


21 ! 


40 


9.70761 


9.93457 


9.77303 


10.22697 


10.06543 


10.29239 


20 


41 


70782 


93450 


77332 


22668 


06550 


29218 


19 


42 


70803 


93442 


77361 


22639 


06558 


29197 


18 


43 


70824 


93435 


77390 


22610 


06565 


29176 


17 


44 


70846 


93427 


77418 


22582 


06573 


29154 


16 


45 


70867 


93420 


77447 


22553 


06580 


29133 


15 


46 


70888 


93412 


77476 


22524 


06588 


29112 


14 


47 


70909 


93405 


77505 


22495 


06595 


29091 


13 


48 


70931 


93397 


77533 


22467 


06603 


29069 


12 


49 


70952 


93390 


77562 


22438 


06610 


29048 


11 


50 


9.70973 


9.93382 


9.77591 


10.22409 


10.06618 


10.29027 


10 


51 


70994 


93375 


77619 


22381 


06625 


29006 


9 


52 


71015 


93367 


77648 


22352 


06633 


28985 


8 


53 
54 


71036 


93360 


77677 


22323 


06640 


28964 


7 


71058 


93352 


77706 


22294 


06648 


28942 


6 


55 


71079 


93344 


77734 


22266 


06656 


28921 


5 


56 


71100 


93337 


77763 


22237 


06663 


28900 


4 


57 


71121 


93329 


77791 


22209 


06671 


28879 


3 


58 


71142 


93322 


77820 


22180 


06678 


28858 


; 


59 


71163 


93314 


77849 


22151 


06686 


28837 


60 


71184 


93307 


77877 


22123 


06693 


28816 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M ' 



59 Degrees 



Artificial Sines, Tang, and Sec. 31 Degrees. 139 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 







9.71184 


9.93307 


9.77877 


10.22123 


10.06693 


10.28816 


60 


1 


71205 


93299 


77906 


22094 


06701 


28795 


59 


2 


71226 


93291 


77935 


22065 


06709 


28774 


58 


3 


71247 


93284 


77963 


22037 


06716 


28753 


57 


4 


71268 


93276 


77992 


22008 


06724 


28732 


56 


5 


71289 


93269 


78020 


21980 


06731 


28711 


55 


6 


71310 


93261 


78049 


21951 


06739 


28690 


54 


7 


71331 


93253 


78077 


21923 


06747 


28669 


53 


8 


71352 


93246 


78106 


21894 


06754 


28648 


52 


9 


71373 


93238 


78135 
9.78163 


21865 
10.21837 


06762 


28627 


51 
50 


10 


9.71393 


9.93230 


10.06770 


10.28607 


11 


71414 


93223 


78192 


21808 


06777 


28586 


49 


12 


71435 


93215 


78220 


21780 


06785 


28565 


48 


13 


71456 


93207 


78249 


21751 


06793 


28544 


47 


14 


71477 


93200 


78277 


21723 


06800 


28523 


46 


15 


71498 


93192 


78306 


21694 


06808 


28502 


45 


16 


71519 


93184 


78334 


21666 


06816 


28481 


44 


17 


71539 


93177 


78363 


21637 


06823 


28461 


43 


18 


71560 


93169 


78391 


21609 


06831 


28440 


42 


19 
20 


71581 
9.71602 


93161 


78419 


21581 


06839 


28419 


41 


9.93154 


9.78448 


10.21552 


10.06846 


10.28398 


40 


21 


71622 


93146 


78476 


21524 


06854 


28378 


39 


22 


71643 


93138 


78505 


21495 


06862 


28357 


38 


23 


71664 


93131 


78533 


21467 


06869 


28336 


37 


24 


71685 


93123 


78562 


21438 


06877 


28315 


36 


25 


71705 


93115 


78590 


21410 


06885 


28295 


35 


. 26 


71726 


93108 


78618 


21382 


06892 


28274 


34 


27 


71747 


93100 


78647 


21353 


06900 


28253 


33 


28 


71767 


93092 


78675 


21325 


06908 


28233 


32 


29 


71788 


93084 


78704 


21296 
10.21268 


06916 


28212 


31 


30 


9.71809 


9.93077 


9.78732 


1C. 06923 


10.28191 


30 


31 


71829 


93069 


78760 


21240 


06931 


28171 


29 


32 


71850 


93061 


78789 


21211 


06939 


28150 


28 


33 


71870 


93053 


78817 


21183 


06947 


28130 


27 


34 


71891 


93046 


78845 


21155 


06954 


28109 


26 


35 


71911 


93038 


78874 


21126 


06962 


28089 


25 


36 


71932 


93030 


78902 


21098 


06970 


28068 


24 


37 


71952 


93022 


78930 


21070 


06978 


28048 


23 


38 


71973 


93014 


78959 


21041 


06986 


28027 


22 


39 


71994 


93007 


78987 


21013 


06993 


28006 


21 
20 


40 


9.72014 


9.92999 


9.79015 


10.20985 


10.07001 


10.27986 


41 


72034 


92991 


79043 


20957 


07009 


27966 


19 


42 


72055 


92983 


79072 


20928 


07017 


27945 


18 


43 


72075 


92976 


79100 


20900 


07024 


27925 


17 


44 


72096 


92968 


79128 


20872 


07032 


27904 


16 


45 


72116 


92960 


79156 


20844 


07040 


27884 


15 


46 


72137 


92952 


79185 


20815 


07048 


27863 


14 


47 


72157 


92944 


79213 


20787 


07056 


27843 


13 


48 


72177 


92936 


79241 


20759 


07064 


27823 


12 


49 


72198 


92929 


79269 


20731 


07071 


27802 


11 


50 


9.72218 


9.92921 


9.79297 


10.20703 


10.07079 


10.27782 


10 


51 


72238 


92913 


79326 


20674 


07087 


27762 


9 


52 


72259 


92905 


79354 


20646 


07095 


27741 


8 


53 


72279 


92897 


79382 


20618 


07103 


27721 


7 


54 


72299 


92889 


79410 


20590 


07111 


27701 


6 


55 


72320 


92881 


79438 


20562 


07119 


27680 


5 


56 


72340 


92874 


79466 


20534 


07126 


27660 


4 


57 


72360 


92866 


79495 


20505 


07134 


27640 


3 


58 


72381 


92858 


79523 


20477 


07142 


27619 


2 


59 


72401 


92850 


79551 


20449 


07150 


27599 


1 


60 


72421 


92842 


79579 


20421 


07158 
Co-secant 


27579 







Co-sine. 


Sine. 


Co-tang:. 


Tangent. 


Secant. 


M. 



58 Degrees. 



140 


Artificial Sines, Tang, and Sec. 32 Degrees. 






M. 


Sine. 
9.72421 


Co-sme. 
9.92842 


Tangent. 
9.79579 


Co-tang. 


Secant. 


Co-secant 









10.20421 


10.07158 


10.27579 


60 




1 


72441 


92834 


79607 


20393 


07166 


27559 


59 




2 


72461 


92826 


79635 


20365 


07174 


27539 


58 




3 


72482 


92818 


79663 


20337 


07182 


27518 


57 




4 


72502 


92810 


79691 


20309 


07190 


27498 


56 




5 


72522 


92803 


79719 


20281 


07197 


27478 


55 




6 


72542 


92795 


79747 


20253 


07205 


27458 


54 




7 


72562 


92787 


79776 


20224 


07213 


27438 


53 




8 


72582 


92779 


79804 


20196 


07221 


27418 


52 




9 


72602 


92771 
9.92763 


79832 


20168 


07229 


27398 


51 
50 




10 


9.72622 


9.79860 


10.20140 


10.07237 


10.27378 




11 


72643 


92755 


79888 


20112 


07245 


27357 


49 




12 


72663 


92747 


79916 


20084 


07253 


27337 


48 




13 


72683 


92739 


79944 


20056 


07261 


27317 


47 




14 


72703 


92731 


79972 


20028 


07269 


27297 


46 




15 


72723 


92723 


80000 


20000 


07277 


27277 


45 




16 


72743 


92715 


80028 


19972 


07285 


27257 


44 




17 


72763 


92707 


80056 


19944 


07293 


27237 


43 




18 


72783 


92699 


80084 


19916 


07301 


27217 


42 




19 


72803 


92691 


80112 
9.80140 


19888 


07309 


27197 
10 27177 


41 




20 


9.72823 


9.92683 


10.19860 


10.07317 


40 




21 


72843 


92675 


80168 


19832 


07325 


27157 


39 




22 


72863 


92667 


80195 


19805 


07333 


27137 


38 




23 


72883 


92659 


80223 


19777 


07341 


27117 


37 




24 


72902 


92651 


80251 


19749 


07349 


27098 


36 




25 


72922 


92643 


80279 


19721 


07357 


27078 


35 




26 


72942 


92635 


80307 


19693 


07365 


27058 


34 




27 


72962 


92627 


80335 


19665 


07373 


27038 


33 




28 


72982 


92619 


80363 


19637 


07381 


27018 


32 




29 


73002 


92611 


80391 


19609 
10.19581 


07389 


26998 


31 
30 




30 


9.73022 


9.92603 


9.80419 


10.07397 


1C 26978 




31 


73041 


92595 


80447 


19553 


07405 


26959 


29 




32 


73061 


92587 


80474 


19526 


07413 


26939 


28 




33 


73081 


92579 


80502 


19498 


07421 


26919 


27 




34 


73101 


92571 


80530 


19470 


07429 


26899 


26 




35 


73121 


92563 


80558 


19442 


07437 


26879 


25 




36 


73140 


92555 


80586 


19414 


07445 


26860 


24 




37 


73160 


92546 


80614 


19386 


07454 


26840 


23 




38 


73180 


92538 


80642 


19358 


07462 


26820 


22 




39 


73200 


92530 


80669 


19331 


07470 


26800 


21 




40 


9.73219 


9.92522 


9.80697 


10.19303 


10.07478 


10.26781 


"20 




41 


73239 


92514 


80725 


19275 


07486 


26761 


19 




42 


73259 


92506 


80753 


19247 


07494 


26741 


18 




43 


73278 


92498 


80781 


19219 


07502 


2672? 


17 




44 


73298 


92490 


80808 


19192 


07510 


26702 


16 




45 


73318 


92482 


80836 


19164 


07518 


26682 


15 




46 


73337 


92473 


80864 


19136 


07527 


26663 


14 




47 


73357 


92465 


80892 


19108 


07535 


26643 


13 




48 


73377 


92457 


80919 


19081 


07543 


26623 


12 




49 


73396 


92449 


80947 


19053 


07551 


26604 


11 




50 


9.73416 


~ <T 92441 


9.80975 


10.19025 


10.07559 


10.26584 


10 




51 


73435 


92433 


81003 


18997 


07567 


26565 


9 




52 


73455 


92425 


8103G 


18970 


07575 


26545 


8 




53 


73474 


92416 


81058 


18942 


07584 


26526 


7 




' 54 


73494 


92408 


81086 


18914 


07592 


26506 


6 




55 


73513 


92400 


81113 


18887 


07600 


26487 


5 




56 


73533 


92392 


81141 


18859 


07608 


26467 


4 




57 


73552 


92384 


81169 


18831 


07616 


26448 


3 




58 


73572 


32376 


81196 


18804 


07624 


26428 


2 




59 


73591 


92367 


81224 


18776 


07633 


26409 


1 




60 


73611 


92359 


81252 


18748 


07641 


26389 









Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M 





57 Degrees. 







Artificial Sines, Tang. 


and Sec. 33 Degrees. 


141 




JI. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 









9.73611 


9.92359 


9.81252 


10.18748 


10.07641 


10.26389 


60 




1 


73630 


92351 


81279 


18721 


07649 


26370 


59 




2 


73650 


92343 


81307 


18693 


07657 


26350 


58 




3 


73669 


92335 


81335 


18665 


07665 


26331 


57 




4 


73689 


92326 


81362 


18638 


07674 


26311 


56 




5 


73708 


92318 


81390 


18610 


07682 


26292 


55 




6 


73727 


92310 


81418 


18582 


07690 


26273 


54 




7 


73747 


92302 


81445 


18555 


07698 


26253 


53 




8 


73766 


92293 


81473 


18527 


07707 


26234 


52 




9 


73785 
9.73805 


92285 


81500 


18500 
10.18472 


07715 
10.07723 


26215 
10.26195 


51 
50 




10 


9.92277 


9.81528 




11 


73824 


92269 


81556 


18444 


07731 


26176 


49 




12 


73843 


92260 


81583 


18417 


07740 


26157 


48 




13 


73863 


92252 


81611 


18389 


07748 


26137 


47 




14 


73882 


92244 


81638 


18362 


07756 


26118 


46 




15 


73901 


92235 


81666 


18334 


07765 


26099 


45 




16 


73921 


92227 


81693 


18307 


07773 


26079 


44 




17 


73940 


92219 


81721 


18279 


07781 


26060 


43 




18 


73959 


92211 


81748 


18252 


07789 


26041 


42 




19 


73978 


92202 


81776 


18224 


07798 


26022 


41 




20 


9.73997 


9.92194 


9.81803 


10.18197 


10.07806 


10.26003 


40 




21 


74017 


92186 


81831 


18169 


07814 


25983 


39 




22 


74036 


92177 


81858 


18142 


07823 


25964 


38 




23 


74055 


92169 


81886 


18114 


07831 


25945 


37 




24 


74074 


92161 


81913 


18087 


07839 


25926 


36 




25 


74093 


92152 


81941 


18059 


07848 


25907 


35 




26 


74113 


92144 


81963 


18032 


07856 


25887 


34 




27 


74132 


92136 


81996 


18004 


07864 


25868 


33 




28 


74151 


92127 


82023 


17977 


07873 


25849 


32 




29 


74170 


92119 


82051 
9.82078 


17949 


07881 


25830 


31 
30 




30 


9.74189 


9.92111 


10.17922 


10.07889 


10.25811 




31 


74208 


92102 


82106 


17894 


07898 


25792 


29 




32 


74227 


92094 


82133 


17867 


07906 


25773 


28 




33 


74246 


92086 


82161 


17839 


07914 


25754 


27 




34 


74265 


92077 


82188 


17812 


07923 


25735 


26 




35 


74284 


92069 


82215 


17785 


07931 


25716 


25 




36 


74303 


92060 


82243 


17757 


07940 


25697 


24 




37 


74322 


92052 


82270 


17730 


07948 


25678 


23 




38 


74341 


92044 


82298 


17702 


07956 


25659 


22 




39 


74360 


92035 


82325 


17675 


07965 


25640 
10.25621 


21 
20 




40 


9.74379 


9.92027 


9.82352 


10.17648 


10.07973 




41 


74398 


92018 


82380 


17620 


07982 


25602 


19 




42 


74417 


92010 


82407 


17593 


07990 


25583 


18 




43 


74436 


92002 


82435 


17565 


07998 


25564 


17 




44 


74455 


91993 


82462 


17538 


08007 


25545 


16 




45 


74474 


91985 


82489 


17511 


08015 


25526 


15 




46 


74493 


91976 


82517 


17483 


08024 


25507 


14 




47 


74512 


91968 


82544 


17456 


08032 


25488 


13 




48 


74531 


91959 


82571 


17429 


08041 


25469 


12 




49 


74549 


91951 


82599 


17401 
10.17374 


08049 
10.08058 


25451 
10.25432 


11 

10 




50 


9.74568 


9.91942 


9.82626 




51 


74587 


91934 


82653 


17347 


08066 


25413 


9 




52 


74606 


91925 


82681 


17319 


08075 


25394 


8 




53 


74625 


91917 


82708 


17292 


08083 


25375 


7 




54 


74644 


91908 


82735 


17265 


08092 


25356 


6 




55 


74662 


91900 


82762 


17238 


08100 


25338 


5 




56 


74681 


91891 


82790 


17210 


08109 


25319 


4 




57 


74700 


91883 


82817 


17183 


08117 


25300 


3 




58 


74719 


91874 


82844 


17156 


08126 


25281 


2 




59 


74737 


91866 


82871 


17129 


08134 


25263 


1 




60 


74756 


91857 


82899 


17101 


08143 


25244 
Secant. 




M. 




1 Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 



SO 



56 Degrees. 



142 


Artificial Sines, Tang 


and Sec. 34 Degrees. 




M. 


Sine. 
~~ 9/74756 


Co-sine. 

9.91857 


Tangent. 
9.82899 


Co-tang. 


Secant. 


Co-secant 




10.17101 


10.08143 


10.25244 


60 


] 1 


74775 


91849 


82926 


17074 


08151 


25225 


59 


2 


74794 


91840 


82953 


17047 


08160 


25206 


58 


3 


74812 


91832 


82980 


17020 


08163 


25188 


57 


4 


74831 


91823 


83008 


16992 


08177 


25169 


56 


5 


74850 


91815 


83035 


16965 


08185 


25150 


55 


6 


74868 


91806 


83062 


16938 


08194 


25132 


54 


7 


74887 


91798 


83089 


16911 


08202 


25113 


53 


8 


74906 


91789 


83117 


16883 


08211 


25094 


52 


9 


74924 


91781 


83144 


16856 


08219 


25076 


51 


10 


9.74943 


9.91772 


9.83171 


10.16829 


10.08228 


10.25057 


50 


11 


74961 


91763 


83198 


16802 


08237 


25039 


49 


12 


74980 


91755 


83225 


16775 


08245 


25020 


48 


13 


74999 


91746 


83252 


16748 


08254 


25001 


47 


14 


75017 


91738 


83280 


16720 


08262 


24983 


46 


15 


75036 


91729 


83307 


16693 


08271 


24964 


45 


16 


75054 


91720 


83334 


16666 


08280 


24946 


44 


17 


75073 


91712 


83361 


16639 


08288 


24927 


43 


18 


75091 


91703 


83388 


16612 


08297 


24909 


42 


19 


75110 


91695 


83415 


16585 


08305 


24890 


41 
40 


20 


9.75128 


9.91686 


9.83442 


10.16558 


10.08314 


10.24872 


21 


75147 


91677 


83470 


16530 


08323 


24853 


39 


22 


75165 


91669 


83497 


16503 


08331 


24825 


38 


23 


75184 


91660 


83524 


16476 


08340 


24816 


37 


24 


75202 


91651 


83551 


16449 


08349 


24798 


36 


25 


75221 


91643 


83578 


16422 


08357 


24779 


35 


26 


75239 


91634 


83605 


16395 


08366 


24761 


34 


27 


75258 


91625 


83632 


16368 


03375 


24742 


33 


28 


75276 


91617 


83659 


16341 


08383 


24724 


32 


29 


75294 


91608 


83686 


16314 


08392 


24706 
10.24687 


31 
30 


30 


9.75313 


9.91599 


9.83713 


10.16287 


10.08401 


31 


75331 


91591 


83740 


16260 


08409 


24669 


29 


32 


75350 


91582 


83768 


16232 


08418 


24650 


28 


33 


75368 


91573 


83795 


16205 


08427 


24632 


27 


34 


75386 


91565 


83822 


16178 


08435 


24614 


26 


35 


75405 


91556 


83849 


16151 


08444 


24595 


25 


36 


75423 


91547 


83876 


16124 


08453 


24577 


24 


37 


75441 


91538 


83903 


16097 


08462 


24559 


23 


33 


75459 


91530 


83930 


16070 


08470 


24541 


22 


39 


75478 


91521 


83957 


16043 


08479 


24522 


21 


40 


9.75496 


9.91512 


9.83984 


10.16016 


10.08488 


10.24504 


20 


41 


75514 


91504 


84011 


15989 


08496 


24486 


19 


42 


75533 


91495 


84038 


15962 


08505 


24467 


18 


43 


75551 


91486 


84065 


15935 


08514 


24449 


17 


44 


75569 


91477 


84092 


15908 


08523 


24431 


16 


45 


75587 


91469 


84119 


15881 


08531 


24413 


15 


46 


75605 


91460 


84146 


15854 


08540 


24395 


14 


47 


75624 


91451 


84173 


15827 


08549 


24376 


13 


48 


75642 


91442 


84200 


15800 


08558 


24358 


12 


49 


75660 


91433 


84227 


15773 


08567 


24340 


11 


50 


9.75678 


9.91425 


9.84254 


10.15746 


10.08575 


10.24322 ! 1 


51 


75696 


91416 


84280 


15720 


08584 


24304 


9 


52 


75714 


91407 


84307 


15693 


08593 


24286 


8 


53 


75733 


91398 


84334 


15666 


08602 


24267 


7 


54 


75751 


91389 


84361 


15639 


08611 


24249 


6 


55 


75769 


91381 


84388 


15612 


08619 


24231 


5 


56 


75787 


91372 


84415 


15585 


08628 


24213 


4 


57 


75805 


91363 


84442 


15558 


08637 


24195 


3 


58 


75823 


91354 


84469 


15531 


08646 


24177 


2 


59 


75841 


91345 


84496 


15504 


08655 


24159 


1 


60 


75859 


91336 


84523 


15477 


08664 


24141 
Secant. 




M. 


1 Co-sine." 


Sine. 


Co-tan^. 


I'^n^ent. 


Co-secant 1 



55 Degrees 



Artificial Sines, Tang, and Sec. 35 Degrees. 143 



j M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. | 


Secant. | 


Co-secant 









9.75859 


9.91336 


9.34523 


10.15477 


10.08664 


10.24141 


60 




1 


75377 


91328 


34550 


15450 


08672 


24123 


59 




2 


75895 


91319 I 


84576 


15424 


08681 


24105 


58 




3 


75913 


91310 


84603 


15397 


08690 


24087 


57 




4 


75931 


91301 


84630 


15370 


08699 


24069 


56 




1 5 


75949 


91292 


84657 


15343 


08708 


24051 


55 




6 


75967 


91283 


84684 


15316 


08717 


24033 


54 




7 


75985 


91274 ; 


84711 


15289 


08726 


24015 


53 




8 


76003 


91263 


84738 


15262 


08734 


23997 


52 




9 
10 


76021 
9.76039 


91257 


84764 


15236 


08743 


23979 
10.23961 


51 
50 




9.91248 


9.84791 


10.15209 


10.08752 




' 11 


76057 


91239 


84818 


15182 


08761 


23943 


49 




12 


76075 


91230 


84845 


15155 


08770 


23925 


48 




13 


76093 


91221 


84872 


15128 


08779 


23907 


47 




14 


76111 


91212 


84899 


15101 


08788 


23889 


46 




15 


76129 


91203 


84935 


15075 


08797 


23871 


45 




16 


76146 


91194 


84952 


15048 


08806 


23854 


44 




17 


76164 


91185 


84979 


15021 


08815 


23836 


43 




18 


76182 


9ir6 


85006 


14994 


08824 


23818 


42 




19 


76200 


91167 
9.91158 


85033 


14967 


08833 


23800 


41 
40 




20 


9.76218 


9.85059 


10.14941 


10.08842 


10.23782 




21 


76236 


91149 


85086 


14914 


08851 


23764 


39 




22 


76253 


91141 


85113 


14887 


03859 


23747 


38 




23 


76271 


91132 


85140 


14860 


08868 


23729 


37 




24 


76289 


91123 


85166 


14334 


08877 


23711 


36 




25 


76307 


91114 


85193 


14807 


08886 


23693 


35 




26 


76324 


91105 


85220 


14780 


08895 


23676 


34 




27 


76342 


91096 


85247 


14753 


08904 


23658 


33 




28 


76360 


91087 


85273 


14727 


08913 


23640 


32 




29 


76378 


91078 


85300 


14700 


08922 


23622 


31 




30 


9.76395 


9.91069 


9.85327 


10.14673 


10.08931 


10.23605 


30 




31 


76413 


91060 


85354 


14646 


08940 


23587 


29 




32 


76431 


91051 


85380 


14620 


08949 


23569 


28 




33 


76448 


91042 


85407 


14593 


08958 


23552 


27 




34 


76466 


91033 


85434 


14566 


08967 


23534 


26 




35 


76484 


91023 


85460 


14540 


08977 


23516 


25 




36 


76501 


91014 


85487 


14513 


08986 


23499 


24 




37 


76519 


91005 


85514 


14486 


08995 


23481 


23 




38 


76537 


90996 


85540 


14460 


09004 


23463 


22 




39 


76554 


90987 


85567 


14433 


09013 


23446 


21 




40 


9.76572 


9.90978 


9.85594 


10.14406 


10.09022 


10.23428 


20 




41 


76590 


90969 


85620 


14380 


09031 


23410 


19 




42 
43 
44 


76607 


90960 


85647 


14353 


09040 


23393 


18 




76625 


90951 


85674 


14326 


09049 


23375 


17 




76642 


90942 


85700 


14300 


09058 


23358 


16 




45 


76660 


90933 


85727 


14273 


09067 


23340 


15 




46 


76677 


90924 


85754 


14246 


09076 


23323 


14 




47 


76695 


90915 


85780 


14220 


09085 


23305 


13 




48 


76712 


90906 


85807 


14193 


09094 


23288 


12 




49 
50 


76730 

9.76747 


90896 


85834 


14166 


09104 
10.09113 


23270 
10.23253 


11 




9.90887 


9.85860 


10.14140 


10 




51 


7f;765 


90878 


85887 


14113 


09122 


23235 


9 




52 


76782 


90869 


85913 


14087 


09131 


23218 


8 




53 


76800 


90860 


85940 


14060 


09140 


23200 


7 




54 


76817 


90851 


85967 


14033 


09149 


23183 


6 




55 


76835 


90842 


85993 


14007 


09158 


23165 


5 




56 


76852 


90832 


86020 


13980 


09168 


23148 


4 




57 


76870 


90823 


86046 


13954 


09177 


23130 


3 




58 


76887 


90814 


86073 


13927 


09186 


23113 


2 




59 


76904 


90805 


86100 


13900 


09195 


23096 


1 




60 


76922 


90796 


86126 


13874 


09204 


23078 









Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 





54 Degree* 



144 Artificial Sines, Tang, and Sec. 36 Degrees. 



M. 


Sine. 


Co-sine. 


Tangent. 
9.86126 


Co-tang. 


Secant. 


Co-secant 


f.O 





9.76922 


9.90796 


10.13874 


10.09204 


10.23078 


1 


76939 


90787 


86153 


13847 


09213 


23061 


59 


2 


76957 


90777 


86179 


13821 


09223 


23043 


58 


3 


76974 


90768 


86206 


13794 


09232 


23026 


57 


4 


76991 


90759 


86232 


13768 


09241 


23009 


56 


5 


77009 


90750 


86259 


13741 


09250 


22991 


55 


6 


77026 


90741 


86285 


13715 


09259 


22974 


54 


7 


77043 


90731 


86312 


13688 


09269 


22957 


53 


8 


77061 


90722 


86338 


13662 


09278 


22939 


52 


9 


77078 


90713 


86365 


13635 


09287 


22922 


51 


•10 


9.77095 


9.90704 


9.86392 


10.13608 


10.09296 


10.22905 


50' 


11 


77112 


90694 


86418 


13582 


09306 


22888 


49 


12 


77130 


90685 


86445 


13555 


09315 


22870 


48 


13 


77147 


90676 


86471 


13529 


09324 


22853 


47 


14 


77164 


90667 


86498 


13502 


09333 


22836 


46 


15 


77181 


90657 


86524 


13476 


09343 


22819 


45 


16 


77199 


90648 


86551 


13449 


09352 


22801 


44 


17 


77216 


90639 


86577 


13423 


09361 


22784 


43 


18 


77233 


90630 


86603 


13397 


09370 


22767 


42 


19 


77250 


90620 


86630 


13370 


09380 


22750 


41 


20 


9.77268 


9.90611 


9.86656 


10.13344 


10.09389 


10.22732 


40 


21 


77285 


90602 


86683 


13317 


09398 


22715 


39 


22 


77302 


90592 


86709 


13291 


09408 


22698 


38 


23 


77319 


90583 


86736 


13264 


09417 


22681 


37 


24 


77336 


90574 


86762 


13238 


09426 


22664 


36 


25 


77353 


90565 


86789 


13211 


09435 


22647 


35 


26 


77370 


90555 


86815 


13185 


09445 


22630 


34 


27 


77387 


90546 


86842 


13158 


09454 


22613 


33 


28 


77405 


90537 


86868 


13132 


09463 


22595 


32 


29 


77422 


90527 


86894 


13106 


09473 


22578 


31 


30 


9.77439 


9.90518 


9.86921 


10.13079 


10.09482 


10-22561 


30 


31 


77456 


90509 


86947 


13053 


09491 


22544 


29 


32 


77473 


90499 


86974 


13026 


09501 


22527 


28 


33 


77490 


90490 


87000 


13000 


09510 


22510 


27 


34 


77507 


90480 


87027 


12973 


09520 


22493 


26 


35 


77524 


90471 


87053 


12947 


09529 


22476 


25 


36 


77541 


90462 


87079 


12921 


09538 


22459 


24 


37 


77558 


90452 


87106 


12894 


09548 


22442 


23 


38 


77575 


90443 


87132 


12868 


09557 


22425 


22 


39 


77592 


90434 


87158 


12842 


09566 


22408 


21 


, 40 


9.77609 


9.90424 


9.87185 


10.12815 


10.09576 


10.22391 


~20~ 


41 


77626 


90415 


87211 


12789 


09585 


22374 


19 


42 


77643 


90405 


87238 


12762 


09595 


22357 


18 


43 


77660 


90396 


87264 


12736 


09604 


22340 


17 


44 


77677 


90386 


87290 


12710 


09614 


22323 


16 


45 


77694 


90377 


87317 


12683 


09623 


22306 


15 


46 


77711 


90368 


87343 


12657 


09632 


22289 


14 


47 


77728 


90358 


87369 


12631 


09642 


22272 


13 


48 


77744 


90349 


87396 


12604 


09651 


22256 


12 


49 


77761 


90339 


87422 


12578 


09661 


22239 
10.22222 


11 
10 


50 


9.77778 


9.90330 


9.87448 


10.12552 


10.09670 


, 51 


77795 


90320 


87475 


12525 


09680 


22205 


9 


52 


77812 


90311 


87501 


12499 


09689 


22188 


8 


53 


77829 


90301 


87527 


12473 


09699 


22171 


7 


54 


77846 


90292 


87554 


12446 


09708 


22154 


6 


55 


77862 


90282 


87580 


12420 


09718 


22138 


5 


56 


77879 


90273 


87606 


12394 


09727 


22121 


4 


57 


77896 


90263 


87633 


12367 


09737 


22104 


3 


58 


77913 


90254 


87659 


12341 


09746 


22087 


2 


59 


77930 


90244 


87685 


12315 


09756 


22070 


1 


60 


77946 


90235 


87711 


12289 


09765 


22054 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Seoant. 


M. 



53 Degrees. 



Artificial Sines, Tang, and Sec. 37 Degrees. 145 



M. 


Sine. 


Co-sine. 
9.90235 


Tangent. 


Co-tang. 


Secant. 


Co-secant 









9.77946 


9.87711 


10.12289 


10.09765 


10.22054 


60 




1 


77963 


90225 


87738 


12262 


09775 


22037 


59 




2 


77980 


90216 


87764 


12236 


09784 


22020 


58 




3 


77997 


90206 


87790 


12210 


09794 


22003 


57 




4 


78013 


90197 


87817 


12183 


09803 


21987 


56 




5 


"8030 


90187 


87843 


12157 


09813 


21970 


55 




6 


78047 


90178 


87869 


12131 


09822 


21953 


54 




7 


78063 


90168 


87895 


12105 


09832 


21937 


53 




8 


78080 


90159 


87922 


12078 


09841 


21920 


52 




9 
10 


78097 
9.78113 


90149 


87948 


12052 


09851 


21903 


51 

50 




9.90139 


9.87974 


10.12026 


10.09861 


10.21887 




11 


78130 


90130 


88000 


12000 


09870 


21870 


49 




12 


78147 


90120 


88027 


11973 


09880 


21853 


48 




13 


78163 


90111 


88053 


11947 


09889 


21837 


47 




14 


78180 


90101 


88079 


11921 


09899 


21820 


46 




15 


78197 


90091 


88105 


11895 


09909 


21803 


45 




16 


78213 


90082 


88131 


11869 


09918 


21787 


44 




17 


78230 


90072 


88158 


11842 


09928 


21770 


43 




18 


78246 


90063 


88184 


11816 


09937 


21754 


42 




19 


78263 


90053 


88210 


11790 


09947 


21737 


41 




20 


9.78280 


9.90043 


9.88236 


10.11764 


10.09957 


10.21720 


40 




21 


78296 


90034 


88262 


11738 


09966 


21704 


39 




22 


78313 


90024 


88289 


11711 


09976 


21687 


38 




23 


78329 


90014 


88315 


11685 


09986 


21671 


37 




24 


78346 


90005 


88341 


11659 


09995 


21654 


36 




. 25 


78362 


89995 


88367 


11633 


10005 


21638 


35 




26 


78379 


89985 


88393 


11607 


10015 


21621 


34 




27 


78395 


89976 


88420 


11580 


10024 


21605 


33 




28 


78412 


89966 


88446 


11554 


10034 


21588 


32 




29 


78428 


89956 


88472 


11528 


10044 


21572 


31 
30 




30 


9.78445 


9.89947 


9.88498 


10.11502 


10.10053 


10.21555 




31 


78461 


89937 


88524 


11476 


10063 


21539 


29 




32 


78478 


89927 


88550 


11450 


10073 


21522 


28 




33 


78494 


89918 


88577 


11423 


10082 


21506 


27 




34 


78510 


89908 


88603 


11397 


10092 


21490 


26 




35 


78527 


89898 


88629 


11371 


10102 


21473 


25 




36 


78543 


89888 


88655 


11345 


10112 


21457 


24 




37 


78560 


89879 


88681 


11319 


10121 


21440 


23 




38 


78576 


89869 


88707 


11293 


10131 


21424 


22 




39 


78592 


89859 


88733 


11267 


10141 


21408 


21 




40 


9.78609 


9.89849 


9.88759 


10.11241 


10.10151 


10.21391 


20 




41 


78625 


89840 


88786 


11214 


10160 


21375 


19 




42 


78642 


89830 


88812 


11188 


10170 


21358 


18 




43 


78658 


89820 


88838 


11162 


10180 


21342 


17 




44 


78674 


89810 


88864 


11136 


10190 


21326 


16 




45 


78691 


89801 


88890 


11110 


10199 


21309 


15 




46 


78707 


89791 


88916 


11084 


10209 


21293 


14 




47 


78723 


89781 


88942 


11058 


10219 


21277 


13 




48 


78739 


89771 


88968 


11032 


10229 


21261 


12 




49 
50 


78756 


89761 


88994 


11006 


10239 


21244 
10.21228 


11 




9.78772 


9.89752 


9.89020 


10.10980 


10.10248 


10 




51 


78788 


89742 


89046 


10954 


10258 


21212 


9 




52 


78805 


89732 


89073 


10927 


10268 


21195 


8 




53 


78821 


89722 


89099 


10901 


10278 


21179 


7 




54 


78837 


89712 


89125 


10875 


10288 


21163 


6 




55 


78853 


89702 


89151 


10849 


10298 


21147 


5 




56 


78869 


89693 


89177 


10823 


10307 


21131 


4 




57 


78886 


89683 


89203 


10797 


10317 


21114 


3 




58 


78902 


89673 


89229 


10771 


10327 


21098 


2 




59 


78918 


89663 


89255 


10745 


10337 


21082 


1 




60 


78934 


89653 


89281 


10719 


10347 


21066 









Co-sinc. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 





36* 



52 Degrees 



3H 



146 Artificial Sines, Tang, and Sec. 38 Degrees. 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 







9.78934 


~~ 9". 89653 


9.89281 


10.10719 


10.10347 


10.21066 


60 


1 


78950 


89643 


89307 


10693 


10357 


21050 


59 


2 


78967 


89633 


89333 


10667 


10367 


21033 


68 


3 


78983 


89624 


89359 


10641 


10376 


21017 


57 


4 


78999 


89614 


89385 


10615 


10386 


21001 


56 


5 


79015 


89604 


89411 


10589 


10396 


20985 


55 


G 


79031 


89594 


89437 


10563 


10406 


20969 


54 


7 


79047 


89584 


89463 


10537 


10416 


20953 


53 


8 


79063 


89574 


89489 


10511 


10426 


20937 


52 


9 


79079 


89564 


89515 


10485 


10436 


20921 


51 


10 


9.79095 


9.89554 


9.89541 


10.10459 


10.10446 


10.20905 | 50 


11 


79111 


89544 


89567 


10433 


10456 


20889 49 


12 


79128 


89534 


89593 


10407 


10466 


20872 48 


13 


79144 


89524 


89619 


10381 


10476 


20856 | 47 


14 


79160 


89514 


89645 


10355 


10486 


20840 | 46 


15 


79176 


89504 


89671 


10329 


10496 


20824 


45 


16 


79192 


89495 


89697 


10303 


10505 


20808 


44 


17 


79208 


89485 


89723 


10277 


10515 


20792 


43 


IB 


79224 


89475 


89749 


10251 


10525 


20776 


42 


19 


79240 


89465 


89775 


10225 
10.10199 


10535 


20760 


41 
40 


20 


9.79256 


9.89455 


9.89801 


10.10545 


10.20744 


21 


79272 


89445 


89827 


10173 


10555 


20728 


39 


22 


79288 


89435 


89853 


10147 


10565 


20712 


38 


23 


79304 


89425 


89879 


10121 


10575 


20696 


37 


24 


79319 


89415 


89905 


10095 


10585 


20681 


36 


23 


79335 


89405 


89931 


10069 


10595 


20665 


35 


26 


79351 


89395 


89957 


10043 


10605 


20649 


34 


27 


79367 


89385 


89983 


10017 


10615 


20633 


33 


28 


79383 


89375 


90009 


09991 


10625 


20617 


32 


29 


79399 


89364 


90035 


09965 


10636 


20601 


31 


30 


9.79415 


9.89354 


9.90061 


10.09939 


10.10646 


10.20585 


30 


31 


79431 


89344 


90086 


09914 


10656 


205C9 


29 


32 


79447 


89334 


90112 


09888 


10666 


20553 


28 


33 


79463 


89324 


90138 


09862 


10676 


20537 


27 


34 


79478 


89314 


90164 


09836 


10686 


20522 


26 


35 


79494 


89304 


90190 


09810 


10696 


20506 


25 


36 


79510 


89294 


90216 


09784 


10706 


20490 


24 


37 


79526 


89284 


90242 


09758 


10716 


20474 


23 


38 


79542 


89274 


90268 


09732 


10726 


20458 i 22 


39 


79558 


89264 


90294 


09706 


10736 


20442 


21 


40 


9.79573 


9.89254 


9.90320 


10.09680 


10.10746 


10.20427 


20 


41 


79589 


89244 


90346 


09654 


10756 


20411 


19 


42 


79605 


89233 


90371 


09629 


10767 


20395 


18 


43 


79621 


89223 


90397 


09603 


10777 


20379 


17 


44 


79636 


89213 


90423 


09577 


10787 


20364 


16 


45 


79652 


89203 


90449 


09551 


10797 


20348 


15 


46 


79668 


89193 


90475 


09525 


10807 


20332 


14 


47 


79684 


89183 


90501 


09499 


10317 


20316 


13 


48 


79699 


89173 


90527 


09473 


10827 


20301 


12 


49 


79715 


89162 


90553 


09447 


10838 


20285 


11 


50 


9.79731 


9.89152 


9.90578 


10.09422 


10.10848 


10.20269 


10 


51 


79746 


89142 


90604 


09396 


10858 


20254 


9 


52 


79762 


89132 


90630 


09370 


10868 


20238 


8 


53 


79778 


89122 


90656 


09344 


10878 


20222 


7 


54 


79793 


89112 


90682 


09318 


10888 


20207 


6 


55 


79809 


89101 


90708 


09292 


10899 


20191 


5 


56 


79825 


89091 


90734 


09266 


10909 


20175 


4 


57 


79840 


89081 


90759 


09241 


10919 


20160 


3 


58 


79856 


89071 


90785 


09215 


10929 


20144 


A : 


59 


79872 


89060 


90811 


09189 


10940 


20128 


1 


60 


79887 


89050 


90837 


09163 


10950 


20113 







Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 


M. 



51 Degrees. 



Artificial Sines, Tang, and Sec. 39 Degrees. 147 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 
10.09163 


Secant. 


Co-secant 







9.79887 


9.89050 


9.90837 


10.10950 


10.20113 


60 


1 


79903 


89040 


90863 


09137 


10960 


20097 


59 


2 


79918 


89030 


90889 


09111 


10970 


20082 


58 


3 


79934 


89020 


90914 


09086 


10980 


20066 


57 


4 


79950 


89009 


90940 


09060 


10991 


20050 


56 


5 


79965 


88999 


90966 


09034 


11001 


20035 


55 


6 


79981 


88989 


90992 


09008 


11011 


20019 


54 


7 


79996 


88978 


91018 


08982 


11022 


20004 


53 


8 


80012 


88968 


91043 


08957 


11032 


19988 


52 , 


9 


80027 


88958 


91069 
9.91095 


08931 
10.08905 


11042 
10.11052 


19973 
10.19957 


51 
50 


10 


9.80043 


9.88948 


11 


80058 


88937 


91121 


08879 


11063 


19942 


49 


12 


80074 


88927 


91147 


08853 


11073 


19926 


48 


13 


80089 


88917 


91172 


08828 


11083 


19911 


47 


14 


80105 


88906 


91198 


08802 


11094 


19895 


46 


15 


80120 


88896 


91224 


08776 


11104 


19880 


45 


16 


80136 


88886 


91250 


08750 


11114 


19864 


44 


17 


80151 


88875 


91276 


08724 


11125 


19849 


43 


18 


80166 


88865 


91301 


08699 


11135 


19834 


42 


19 
20 


80182 
9.80197 


88855 


91327 
9.91353 


08673 


11145 


19818 


41 
40 


9.88844 


10.08647 


10.11156 


10.19803 


21 


80213 


88834 


91379 


08621 


11166 


19787 


39 


22 


80228 


88824 


91404 


08596 


11176 


19772 


38 


23 


80244 


88813 


91430 


08570 


11187 


19756 


37 


24 


80259 


88803 


91456 


08544 


11197 


19741 


36 


25 


80274 


88793 


91482 


08518 


11207 


19726 


35 


26 


80290 


88782 


91507 


08493 


11218 


19710 


34 


27 


80305 


88772 


91533 


08467 


11228 


19695 


33 


28 


80320 


88761 


91559 


08441 


11239 


19680 


32 


29 


80336 


88751 


91585 


08415 


11249 


19664 
10.19649 


31 

30 


30 


9.80351 


9.88741 


9.91610 


10.08390 


10.11259 


31 


80366 


88730 


91636 


08364 


11270 


19634 


29 


32 


80382 


88720 


91662 


08338 


11280 


19618 


28 


33 


80397 


88709 


91688 


08312 


11291 


19603 


27 


34 


80412 


88699 


91713 


08287 


11301 


19588 


26 


35 


80428 


88688 


91739 


08261 


11312 


19572 


25 


36 


80443 


88678 


91765 


08235 


11322 


19557 


24 


37 


80458 


88668 


91791 


08209 


11332 


19542 


23 


38 


80473 


88657 


91816 


08184 


11343 


19527 


22 


39 


80489 


88647 


91842 


08158 


11353 


19511 


21 
20 


40 


9.80504 


9.88636 


9.91868 


10.08132 


10.11364 


10.19496 


41 


80519 


88626 


91893 


08107 


11374 


19481 


19 


42 


80534 


88615 


91919 


08081 


11385 


19466 


18 


43 


80550 


88605 


91945 


08055 


11395 


19450 


17 


44 


80565 


88594 


91971 


08029 


11406 


19435 


16 


45 


80580 


88584 


91996 


08004 


11416 


19420 


15 


46 


80595 


88573 


92022 


07978 


11427 


19405 


14 


47 


80610 


88563 


92048 


07952 


11437 


19390 


13 


48 


80625 


88552 


92073 


07927 


11448 


19375 


12 


49 


80641 


88542 


92099 


07901 


11458 
10.11469 


19359 


11 
10 


50 


9.80656 


9.88531 


9.92125 


10.07875 


10.19344 


51 


80671 


88521 


92150 


07850 


11479 


19329 


9 


52 


80686 


88510 


92176 


07824 


11490 


19314 


8 


53 


80701 


88499 


92202 


07798 


11501 


19299 


7 


54 


80716 


88489 


92227 


07773 


11511 


19284 


6 


55 


80731 


88478 


92253 


07747 


11522 


19269 


5 


56 


80746 


88468 


92279 


07721 


11532 


19254 


4 


57 


80762 


88457 


92304 


07696 


11543 


19238 


3 


58 


80777 


88447 


92330 


07670 


11553 


19223 


2 


59 


80792 


88436 


92356 


07644 


11564 


19208 


1 


60 


80807 


88425 


92381 


07619 


11575 


19193 




M. 




Co-sine. 


Sine. " 


Co-tang. 


Tangent. 


Co-secant 


Secant. 



50 Degrees. 



148 Artificial Sines, Tang, and Sec. 40 Degrees 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 
10.07619 


Secant. 


Co-secant 


60 





9.80807 


9.88425 


9.92381 


10.11575 


10.19193 


1 


80822 


88415 


92407 


07593 


11585 


19178 


59 


2 


80837 


88404 


92433 


07567 


11596 


19163 


58 


3 


80852 


88394 


92458 


07542 


11606 


19148 


57 


4 


80867 


88383 


92484 


07516 


11617 


19133 


56 


5 


80882 


88372 


92510 


07490 


11628 


19113 


55 


6 


80897 


88362 


92535 


07465 


11638 


19103 


54 


7 


80912 


88351 


92561 


07439 


11649 


19088 


53 


8 


80927 


88340 


92587 


07413 


11660 


19073 


52 


9 
10 


80942 
9.80957 


88330 


92612 


07388 


11670 


19058 


51 


9.88319 


9.92638 


10 07362 


10.11681 


10.19043 


50" 


11 


80972 


88308 


92663 


07337 


11692 


19028 1 49 


12 


80987 


88298 


92689 


07311 


11702 


19013 


48 


13 


81002 


88287 


92715 


07285 


11713 


18998 


47 


14 


81017 


88276 


92740 


07260 


11724 


18983 


46 


15 


81032 


88266 


92766 


07234 


11734 


18968 


45 


16 


81047 


88255 


92792 


07208 


11745 


18953 


44 


17 


81061 


88244 


92817 


07183 


11756 


18939 


43 


18 


81076 


88234 


92843 


07157 


11766 


18924 


42 


19 


81091 


88223 


92868 


07132 


11777 


18909 


41 


20 


9.81106 


9.88212 


9.92894 


10.07106 


10.11788 


10.18894 


40 


21 


81121 


88201 


92920 


07080 


11799 


18879 


39 


22 


81136 


88191 


92945 


07055 


11809 


18864 


38 


23 


81151 


88180 


92971 


07029 


11820 


18849 


37 


24 


81166 


88169 


92996 


07004 


11831 


18834 


36 


25 


81180 


88158 


93022 


06978 


11842 


18820 


35 


26 


81195 


88148 


93048 


06952 


11852 


18805 


34 


27 


81210 


88137 


93073 


06927 


11863 


18790 


33 


28 


81225 


88126 


93099 


06901 


11874 


18775 


32 


29 
30 


81240 
9.81254 


88115 


93124 
9.93150 


06876 


11885 


18760 


31 


9.88105 


10.06850 


10.11895 


10.18746 


SO 


31 


81269 


88094 


93175 


06825 


11906 


18731 


29 


32 


81284 


88083 


93201 


06799 


11917 


18716 


28 


33 


81299 


88072 


93227 


06773 


11928 


18701 


27 


34 


81314 


88061 


93252 


06748 


11939 


18686 


26 


35 


81328 


88051 


93278 


06722 


11949 


18672 


25 


36 


81343 


88040 


93303 


06697 


11960 


18657 


24 


37 


81358 


88029 


93329 


06671 


11971 


18642 


23 


38 


81372 


88018 


93354 


06646 


11982 


18628 


22 


39 


81387 


88007 


93380 


06620 


11993 


18613 


21 


40 


9.81402 


9.87996 


9.93406 


10.06594 


10.12004 


10.18598 


20 


41 


81417 


87985 


93431 


06569 


12015 


18583 


19 


42 


81431 


87975 


93457 


06543 


12025 


18569 


18 


43 


81446 


87964 


93482 


06518 


12036 


18554 


17 


44 


81461 


87953 


93508 


06492 


12047 


18539 


16 


45 


81475 


87942 


93533 


06467 


12058 


18525 


15 


46 


81490 


87931 


93559 


06441 


12069 


18510 


14 


47 


81505 


87920 


93584 


06416 


12080 


18495 


13 


48 


81519 


87909 


93610 


06390 


12091 


18481 


12 


49 


81534 


87898 


93636 


06364 


12102 


18466 


11 


50 


9.81549 


9.87887 


9.93661 


10.06339 


10.12113 


10.18451 


10 


51 


81563 


87877 


93687 


06313 


12123 


18437 


9 


52 


81578 


87866 


93712 


06288 


12134 


18422 


8 


53 


81592 


87855 


93738 


06262 


12145 


18408 


7 


54 


81607 


87844 


93763 


06237 


12156 


18393 


6 


55 


81622 


87833 


93789 


06211 


12167 


18378 


5 


56 


81636 


87822 


93814 


06186 


12178 


18364 


4 


57 


81651 


87811 


93840 


06160 


12189 


18349 


3 


58 


81665 


87800 


93865 


06135 


12200 


18335 


2 


59 


81680 


87789 


93891 


06109 


12211 


18320 


1 


60 


81694 


87778 


93916 


06084 


12222 
Co-secant 


18306 


° 


'■ Cn-=ino. 


Sine. 


Co-Ian?. 


Tangent. 


Secant. : M. :] 



49 Decrees. 



Artificial Sines, Tang, and Sec. 41 Degrees. 149 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 
10.12222 


Co-secant 
10.18306 


60 





9.81694 


9.87778 


9.93916 


10.06084 


1 


81709 


87767 


93942 


06058 


12233 


18291 


59 


2 


81723 


87756 


93967 


06033 


12244 


18277 


53 


3 


81738 


87745 


93993 


06007 


12255 


18262 


57 


4 


81752 


87734 


94018 


05982 


12266 


18248 


56 


5 


81767 


87723 


94044 


05956 


12277 


18233 


55 


6 


81781 


87712 


94069 


05931 


12288 


18219 


54 


7 


81796 


87701 


94095 


05905 


12299 


18204 


53 


8 


81810 


87690 


94120 


05880 


12310 


18190 


52 


9 


81825 


87679 


94146 


05854 


12321 


18175 


51 
50 


10 


9.81839 


9.87668 


9.94171 


10.05829 


10.12332 


10.18161 


11 


81854 


87657 


94197 


05803 


12343 


18146 


49 


12 


81868 


87646 


94222 


05778 


12354 


18132 


48 


13 


81882 


87635 


94248 


05752 


12365 


18118 


47 


14 


81897 


87624 


94273 


05727 


12376 


18103 


46 


15 


81911 


87613 


94299 


05701 


12387 


18089 


45 


1 16 


81926 


87601 


94324 


05676 


12399 


18074 


44 


17 


81940 


87590 


94350 


05650 


12410 


18060 


43 


13 


81955 


87579 


94375 


05625 


12421 


18045 


42 


19 


81969 


87568 


94401 


05599 


12432 


18031 


41 


20 


9.81983 


9.87557 


9.94426 


10.05574 


10.12443 


10.18017 


40 


21 


81998 


87546 


94452 


05548 


12454 


18002 


39 


1 22 


82012 


87535 


94477 


05523 


12465 


17988 


38 


1 23 


82026 


87524 


94503 


05497 


12476 


17974 


37 


| 24 


82041 


87513 


94528 


05472 


12487 


17959 


36 


25 


82055 


87501 


94554 


05446 


12499 


17945 


35 


26 


82069 


87490 


94579 


05421 


12510 


17931 


34 


27 


82084 


87479 


94604 


05396 


12521 


17916 


33 


28 


82098 


87468 


94630 


05370 


12532 


17902 


32 


29 


82112 


87457 


94655 


05345 


12543 


17888 


31 


30 


9.82126 


9.87446 


9.94681 


10.05319 


10.12554 


10.17874 


30 


31 


82141 


87434 


94706 


05294 


12566 


17859 


29 


32 


82155 


87423 


94732 


05268 


12577 


17845 


28 


33 


82169 


87412 


94757 


05243 


12588 


17831 


27 


34 


32184 


87401 


94783 


05217 


12599 


17816 


26 


35 


82198 


87390 


94808 


05192 


12610 


17802 


25 


36 


82212 


87378 


94834 


05166 


12622 


17788 


24 


37 


82226 


87367 


94859 


05141 


12633 


17774 


23 


38 


82240 


87356 


94884 


05116 


12644 


17760 


22 


39 


82255 


87345 


94910 


05090 


12655 


17745 


21 


40 


9.82269 


9.87334 


9.94935 


10.05065 


10.12666 


10.17731 


20 


41 


82283 


87322 


94961 


05039 


12678 


17717 


19 


42 


82297 


87311 


94986 


05014 


12689 


17703 


18 


43 


82311 


87300 


95012 


04988 


12700 


17689 


17 


44 


82326 


87288 


95037 


04963 


12712 


17674 


16 


45 


8234C 


87277 


95062 


04938 


12723 


17660 


15 


46 


82354 


87266 


95088 


04912 


12734 


17646 


14 


47 


82368 


87255 


95113 


04887 


12745 


17632 


13 


48 


82382 


87243 


95139 


04861 


12757 


17618 


12 


49 
50 


82396 
9.8241C 


87232 
9.87221 


95164 


04836 


12768 


17604 


11 
10 


9.95190 


10.04810 


10.12779 


10.17590 


51 


82424 


87209 


95215 


04785 


12791 


17576 


9 


52 


82439 


87198 


95240 


04760 


12802 


17561 


8 


53 


82453 


87187 


95266 


04734 


12813 


17547 


7 


54 


82467 


87175 


95291 


04709 


12825 


17533 


6 


55 


82481 


87164 


95317 


04683 


12836 


17519 


5 


56 


82495 


87153 


95342 


04658 


12847 


17505 


4 


57 


82509 


87141 


95368 


04632 


12859 


17491 


3 


58 


82523 


87130 


95393 


04607 


12870 


17477 


2 


59 


82537 


87119 


95418 


04582 


12881 


17463 


1 


60 


82551 


87107 


95444 


04556 


12893 


17449 



M. 


1 ^o-sine. 


Sine. 


Co-tan?. 


Tansrent. 


Co-secant 


Secant. 



48 n< 



150 Artificial Sines, Tang, and Sec. 42 Degrees. 



M. 


Sine. 


Co-sine. 


Tangent. 


Co-tano;. 
10.04556 


Secant. 


Co-secant 
"10.17449 


6Cf 







9.82551 


9-87107 


9.95444 


10.12893 




1 


82565 


87096 


95469 


04531 


12904 


17435 


59 




2 


82579 


87085 


95495 


04505 


12915 


17421 


58 




3 


82593 


87073 


95520 


04480 


12927 


17407 


57 




4 


82607 


87062 


95545 


04455 


12938 


17393 


56 




5 


82621 


87050 


95571 


04429 


12950 


17379 


55 




6 


82635 


87039 


95596 


04404 


12961 


17365 


54 




7 


82649 


87028 


95622 


04378 


12972 


17351 


53 




8 


82663 


87016 


95647 


04353 


12984 


17337 


52 




9 


82677 


87005 


95672 


04328 


12995 


17323 


51 
50 




10 


9.82691 


9.86993 


9.95698 


10.04302 


10.13007 


10.17309 




11 


82705 


86982 


95723 


04277 


13018 


17295 


49 




12 


82719 


86970 


95748 


04252 


13030 


17281 


48 




13 


82733 


86959 


95774 


04226 


13041 


17267 


47 




14 


82747 


86947 


95799 


04201 


13053 


17253 


46 




15 


82761 


86936 


95825 


04175 


13064 


17239 


45 




16 


82775 


86924 


95850 


04150 


13076 


17225 


44 




17 


82788 


86913 


95875 


04125 


13087 


17212 


43 




18 


82802 


86902 


95901 


04099 


13098 


17198 


42 




19 


82816 


86890 


95926 


04074 


13110 


17184 


41 




20 


9.82830 


9.86879 


9.95952 


10.04048 


10.13121 


10.17170 


40 




21 


82844 


86867 


95977 


04023 


13133 


17156 


39 




22 


82858 


86855 


96002 


03998 


13145 


17142 


38 




23 


82872 


86844 


96028 


03972 


13156 


17128 


37 




24 


82885 


86832 


96053 


03947 


13168 


17115 


36 




25 


82899 


86821 


96078 


03922 


13179 


17101 


35 




26 


82913 


86809 


96104 


03896 


13191 


17087 


34 




27 


82927 


86798 


96129 


03871 


13202 


17073 


33 




28 


82941 


86786 


96155 


03845 


13214 


17059 


32 




29 


82955 


86775 
9.86763 


96180 
9.96205 


03820 


13225 


17045 


31 




30 


9.82968 


10.03795 


10.13237 


10.17032 


30 




31 


82982 


86752 


96231 


03769 


13248 


17018 


29 




32 


82996 


86740 


96256 


03744 


13260 


17004 


28 




33 


83010 


86728 


96281 


03719 


13272 


16990 


27 




34 


83023 


86717 


96307 


03693 


13283 


16977 


26 




35 


83037 


86705 


96332 


03668 


13295 


16963 


25 




36 


83051 


86694 


96357 


03643 


13306 


16949 


24 




37 


83065 


86682 


96383 


03617 


13318 


16935 


23 




33 


83078 


86670 


96408 


03592 


13330 


16922 


22 




39 


83092 


86659 


96433 


03567 


13341 
10.13353 


16908 
10.16894 


21 




40 


. .83106 


9.86647 


9.96459 


10.03541 


20 




41 


83120 


86635 


96484 


03516 


13365 


16880 


19 




42 


83133 


86624 


96510 


03490 


13376 


16867 


18 




43 


83147 


86612 


96535 


03465 


13388 


16853 


17 




44 


83161 


86600 


96560 


03440 


13400 


16839 


16 




45 


83174 


86589 


96586 


03414 


13411 


16826 


15 




46 


83188 


86577 


96611 


03389 


13423 


16812 


14 




47 


83202 


86565 


96636 


03364 


13435 


16798 


13 




48 


83215 


86554 


96662 


03338 


13446 


16785 


12 




49 


83229 


86542 


96687 


03313 


13458 


16771 


11 




50 


y. 83242 


9.86530 


9.96712 


10.03288 


10.13470 


10.16758 


10 




51 


83256 


86518 


96738 


03262 


13482 


16744 


9 




52 


83270 


86507 


96763 


03237 


13493 


16730 


8 




53 


83283 


86495 


96788 


03212 


13505 


16717 


7 




54 


83297 


86483 


96814 


03186 


13517 


16703 


6 




55 


83310 


86472 


96839 


03161 


13528 


16690 


5 




56 


83324 


86460 


96864 


03136 


13540 


16676 


4 




57 


83338 


86448 


96890 


03110 


13552 


16662 


3 




58 


83351 


86436 


96915 


03085 


13564 


16649 


2 




59 


83365 


86425 


96940 


03060 


13575 


16635 


1 




60 


83378 


86413 


96966 


03034 


13587 


16622 









Co-sine. 


Sin*. 


Co-tan$. 


Tangent. 


Co-secant 


Secant. M. 





41 Degrees. 



Artificial Sines, Tang, and Sec. 43 Degrees. 151 



M. 


bine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant | 





9.83378 


9.86413 


9.96966 


10.03034 


10.13587 


10.16622' 60 


1 


83392 


86401 


96991 


03009 


13599 


16608 1 59 


2 


83405 


86389 


97016 


02984 


13611 


16595 


58 


3 


83419 


86377 


97042 


02958 


13623 


16581 


57 


4 


83432 


86366 


97067 


02933 


13634 


16568 


56 


5 


83446 


86354 


97092 


02908 


13646 


16554 


55 


6 


83459 


86342 


97118 


02882 


13658 


16541 


54 


7 


83473 


86330 


97143 


02857 


13670 


16527 


53 


8 


83486 


86318 


97168 


02832 


13682 


16514 


52 


9 


83500 
9.83513 


86306 


97193 


02807 


13694 


16500 


51 
50 


10 


9.86295 


9.97219 


10.02781 


10.13705 


10.16487 


11 


83527 


86283 


97244 


02756 


13717 


16473 


49 


12 


83540 


86271 


97269 


02731 


13729 


16460 


48 


13 


83554 


86259 


97295 


02705 


13741 


16446 


47 


14 


83567 


86247 


97320 


02680 


13753 


16433 


46 


15 


83581 


86235 


97345 


02655 


13765 


16419 


45 


16 


83594 


86223 


97371 


02629 


13777 


16406 


44 


17 


83608 


86211 


97396 


02604 


13789 


16392 


43 


18 


83621 


86200 


97421 


02579 


13800 


16379 


42 


19 


83634 


86188 


97447 


02553 


13812 


16366 


41 

40 


20 


9.83648 


9.86176 


9.97472 


10.02523 


10.13824 


10.16352 


■ 21 


83661 


86164 


97497 


02503 


13836 


16339 


39 


22 


83674 


86152 


97523 


02477 


13348 


16326 


38 


23 


83688 


86140 


97548 


02452 


13860 


16312 


37 


24 


83701 


86128 


97573 


02427 


13872 


16299 


36 


25 


83715 


86116 


97598 


02402 


13884 


16285 


35 


26 


83728 


86104 


97624 


02376 


13896 


16272 


34 


27 


83741 


86092 


97649 


02351 


13908 


16259 


33 


28 


83755 


86080 


97674 


02326 


13920 


16245 


32 


29 


83768 


86068 


97700 


02300 


13932 


16232 


31 


30 


9.83781 


9.86056 


9.97725 


10.02275 


10.13944 


10.16219 


30 


31 


83795 


86044 


97750 


02250 


13956 


16205 


29 


32 


83808 


86032 


97776 


02224 


13968 


16192 


28 


33 


83821 


86020 


97801 


02199 


13980 


16179 


27 


34 


83834 


86008 


97826 


02174 


13992 


16166 


2( 


35 


83848 


85996 


97851 


02149 


14004 


16152 


2.' 


36 


83861 


85984 


97877 


02123 


14016 


16139 


24 


37 


83874 


85972 


97902 


02098 


14028 


16126 


23 


38 


83887 


85960 


97927 


02073 


14040 


16113 


22 


39 


83901 


85948 
9.85936 


97953 


02047 


14052 


16099 


%. 


40 


9.83914 


9.97978 


10.02022 


10.14064 


10.16086 


20 


41 


83927 


85924 


98003 


01997 


14076 


16073 


19 


42 


83940 


85912 


98029 


01971 


14088 


16060 


18 


43 


83954 


85900 


98054 


01946 


14100 


16046 


17 ' 


44 


83967 


85888 


98079 


01921 


14112 


16033 


16 


45 


83980 


85876 


98104 


01896 


14124 


16020 


15 


1 46 


83993 


85864 


98130 


01870 


14136 


16007 


14 


47 


84006 


85851 


98155 


01845 


14149 


15994 


13 


48 


84020 


85839 


98180 


01820 


14161 


15980 


12 


49 


84033 
8. 84046 


85827 
9.85815 


98206 


01794 


14173 


15967 


11 


50 


9.98231 


10.01769 


10.14185 


10-15954 


10 


51 


84059 


85803 


98256 


01744 


14197 


15941 


9 


52 


84072 


85791 


98281 


01719 


14209 


15928 


8 


53 


84085 


85779 


98307 


01693 


14221 


15915 


7 


54 


84098 


85766 


98332 


01668 


14234 


15902 


6 


55 


84112 


85754 


98357 


01643 


14246 


15888 


5 


56 


84125 


85742 


98383 


01617 


14258 


15875 


4 


57 


84138 


85730 


98408 


01592 


14270 


15862 


3 


58 


84151 


85718 


98433 


01567 


14282 


15849 


2 


59 


84164 


85706 


98458 


01542 


14294 


15836 


1 


60 


84177 


85693 


98484 


01516 


14307 


15823 



M. 




Co-sine. 


Sine. 


Co-tang. 


Tangent. 


Co-secant 


Secant. 



46 Degrees. 





112 

5 



152 


Artificial Sines, Tang. 


and Sec. 44 De 


grees. 




|M. 


Sine. 


Co-sine. 


Tangent. 


Co-tang. 


Secant. 


Co-secant 


60 


i ° 


9.84177 


9.85693 


9.98484 


10.01516 


10.14307 


10.15823 


1 


84190 


85681 


98509 


01491 


14319 


15810 


59 


1 2 


84203 


85669 


98534 


01466 


14331 


15797 


58 


3 


84216 


85657 


98560 


01440 


14343 


15784 


57 


4 


84229 


85645 


98585 


01415 


14355 


15771 


56 


5 


84242 


85632 


98610 


01390 


14368 


15758 


55 


6 


84255 


85620 


98635 


01365 


14380 


15745 


54 


7 


84269 


85608 


98661 


01339 


14392 


15731 


53 


8 


84282 


85596 


98686 


01314 


14404 


15718 ! 52 


9 
10 ' 


84295 


85583 
9.85571 


98711 


01289 


14417 


15705 


51 
50" 


9.84308 


9.98737 


10.01263 


10.14429 


10.15692 


11 


84321 


85559 


98762 


01238 


14441 


15679 


49 


12 


84334 


85547 


98787 


01213 


14453 


15666 


48 


13 


84347 


85534 


98812 


01188 


14466 


15653 


47 


14 


84360 


85522 


98838 


01162 


14478 


15640 


46 


15 


84373 


85510 


98863 


01137 


14490 


15627 


45 


16 


84385 


85497 


98888 


01112 


14503 


15615 


44 


17 


84398 


85485 


98913 


01087 


14515 


15602 


43 


18 


84411 


85473 


98939 


01061 


14527 


15589 


42 


19 


84424 


85460 


98964 


01036 


14540 


15576 


41 


20 


9.84437 


9.85448 


9.98989 


10.01011 


10.14552 


10.15563 


40 


21 


84450 


85436 


99015 


00985 


14564 


15550 


39 


22 


84463 


85423 


99040 


00960 


14577 


15537 


38 


23 


84476 


85411 


99065 


00935 


14589 


15524 


37 


24 


84489 


85399 


99090 


00910 


14601 


15511 


36 


25 


84502 


85386 


99116 


00884 


14614 


15498 


35 


26 


84515 


85374 


99141 


00859 


14626 


15485 


34 


27 


84528 


85361 


99166 


00834 


14639 


15472 


33 


28 


84540 


85349 


99191 


00809 


14651 


15460 


32 


29 


84553 


85337 


99217 


00783 


14663 


15447 


31 


30 


9.84566 


9.85324 


9.99242 


10.00758 


10.14676 


10.15434 


30 


31 


84579 


85312 


99267 


00733 


14688 


15421 


29 


32 


84592 


85299 


99293 


00707 


14701 


15408 


28 


33 


84605 


85287 


99318 


00682 


14713 


15395 


27 


34 


84618 


85274 


99343 


00657 


14726 


15382 


26 


35 


84630 


85262 


99368 


00632 


14738 


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25 


36 


84643 


85250 


99394 


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14750 


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24 


37 


84656 


85237 


99419 


00581 


14763 


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23 


38 


84669 


85225 


99444 


00556 


14775 


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22 


39 


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21 
20 


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9.99495 


10.00505 


10.14800 


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41 


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85187 


99520 


00480 


14813 


15293 


19 


42 


84720 


85175 


99545 


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18 


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848 


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848 


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849 


58 


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Co-sini 



•■a 



152 



BOOKS 

PUBLISHED BY 

URIAH HUNT & SON, 

AND FOR SALE AT THEIR CHEAP BOOK-STORE, 
No. 4i NORTH FOURTH STREET, PHIL AD. 



COMPRISE 3 



SCHOOL, MISCELLANEOUS, AN3 CLASSICAL BOOKS. 



School Teachers and those having care of children are particularly invited to examine 
this list, as it includes many books unequalled for educational purposes. 

The Classical Student will find in it several leading Latin looks, and the general 
reader will meet with much that is standard and good in literature. 

Country Merchants and Booksellers are supplied on the most liberal terms with every 
thing the market affords in the book line. 

Orders for Books and Stationery are solicited, and will receive prompt attention. 



THE HOME BOOK OF HEALTH AND MEDICINE. A po- 

pular treatise on the means of avoiding and curing diseases, and of preserving 
the health and vigour of the body to the latest period. 8vo, 630 pp. 

The author of this work is well known to his professional brethren in Philadelphia, as 
a man of great industry, excellent judgment, and extensive practical experience. These 
qualifications have been united in producing the " Home Book of Health and Medi- 
cine ;" and as families resident in the country, and persons who make long sea voyages, 
require some aid in treating the emergencies of disease, we have much pleasure and 
confidence in recommending this book as the most judicious of its kind that has come 
under our notice. It embraces a brief but luminous view of the various branches of 
medical science, and may be read with advantage, not only by those who have the 
responsible charge of invalids, but also by young men who are about commencing 
their medical studies, and who stand in need of a plain and comprehensive view of the 
healing art. SAMUEL GEORGE MORTON, M. D., 

Professor of Anatomy in Penn'a Medical College, <£-c. #c 
_ We have great pleasure in recommending " The Home Book of Health and Medi- 
cine" as the best popular treatise upon practical medicine with which we are acquainted. 
W. W. GERHARD, M. D., 7 m 7 , 7 , 
JAMES A. M'CREA, M. D., $ ^^delphta. 

GODMAN'S AMERICAN NATURAL HISTORY. 8vo. It is 

illustrated by 125 copperplate engravings of animals, unsurpassed for their fidelity to 

nature. 8vo, 682 pp. 

Of this work the author's biographer states, " Of his works, not immediately con 
nected with his profession, his Natural History of American Quadrupeds is the most 
elaborate. This production will long remain a splendid monument of the genius and 
industry of its author, and be regarded as a model of composition for works of that de- 
scription. It should have a place upon the table of every family, and be put into the 
hands of all the youth of our country." It contains also Godman's Rambles of a 
Naturalist, a highly interesting and instructive book. 

1 



THE LIFE OF BENJAMIN FRANKLIN. With many cnoice 

anecdotes and admirable sayings of this great man, never before published by any 
of his biographers. By M. L. Weems, author of Life ofPenn, &c. 12mo, 239 pp. 

This is a capital book, written in a style abounding in wit and humour, full of 
incidents in both the public and private life of Dr. Franklin, and containing extracts 
from most of his published writings. 

THE LIFE OF WILLIAM PENN, the settler of Pennsylvania, 

the founder of Philadelphia, and one of the first lawgivers in the colonies; con- 
taining also his celebrated treaty with the Indians, his purchase of their country, 
valuable anecdotes of Admiral Penn, also of King Charles II., King James II., King 
William and Queen Anne, (in whose reigns William Penn lived,) curious circum- 
stances that led him to become a Quaker. With a view of the admirable traits in 
the character of the people called Friends or Quakers, who have done so much to me- 
liorate the condition of suffering humanity. To which is added the Reflections and 
Maxims of Penn. By M. L. Weems, author of the Life of Franklin, &c. 12mo, 282 pp 

JAY'S FAMILY PRAYERS. Bound in neat cloth. 18mo, 249 pp. 
DODDRIDGE'S RISE AND PROGRESS OF RELIGION IN 

THE SOUL. 18mo, 288 pp. 

THE AMERICAN FARRIER; containing a minute account of the 

formation of every part of the horse, from the extremity of the head to the hoof, with 
a description of the diseases to which each part is liable, the best remedies to be 
applied in effecting a cure, and the most approved methods of treatment for preventing 
disorders. 12mo, 286 pp. 

BAXTER'S CALL TO THE UNCONVERTED. Bound in neat 

cloth. 18mo, 240 pp. 

GOULD'S SYSTEM OF STENOGRAPHY; or, THE ART OF 

SHORT-HAND WRITING. 18mo, 60 pp. 

HAZEN'S PANORAMA OF TRADES AND PROFESSIONS-, 

or, EVERY MAN'S BOOK. Embellished with 82 engravings. 12mo, 320 pp. 

The object of this book is to give the history of the ordinary trades and professions of 
men, with a description of the mode of working or manufacture used in producing the 
various articles used in common life. It is calculated to add much to the intelligence of 
all, particularly the young, and increase their desire to know and capacity to learn. 
The use of books like this and the Book of Commerce, as reading books in classes, 
while at the same time they afford good reading exercises, will impart a great amount 
of knowledge concerning the affairs of common life, which is of inestimable value. 

THE BOOK OF COMMERCE BY SEA AND LAND; 

exhibiting its connection with Agriculture, the Arts, and Manufactures. 12mo, 185 pp. 

In this work the learner is made acquainted with the origin, mode of manufacture, and 
history of all the articles used in daily life. It treats of the articles of food, furs, woods, 
metals, minerals, fisheries, glass-ware, China, pottery, drugs, banks, customs, tariff". 
Aistory of commerce, &c. It is used in the best schools in New England, the city 
of Philadelphia, and other parts of the Union. 

SUPER-ROYAL OXFORD OCTAVO BIBLE. Bound in sheep 

The most beautiful edition of the Bible published. 

This edition of the Bible is printed on a beautiful large type, incomparably more 
convenient for family use than the cumbrous quartos. The utmost care has been 
used to have it free from typographical errors. It is believed to approach nearer to 
perfection than any Bible extant and sold at a low price. 



SCHOOL EDITIONS OF MILTON'S PARADISE LOST, POL- 

LOK'S COURSE OF TIME, YOUNG'S NIGHT THOUGHTS, COW- 

PER'S TASK, and THOMSON'S SEASONS. 18mo. • 

These will be found the cheapest and best school editions of those authors published. 

THE UNIVERSAL CLASS-BOOK. By T. Hughs. 

This work contains a selection of the best specimens of the best English and Ame- 
rican authors, and is offered at a price considerably less than that of any similar book in 
the market. 

THE LIBRARY OF POETS; containing the works of the most 

prominent English Poets, and selections from American authors, as follows; — 

Scott's Ballads and other Poems; Campbell's Poems; Young's Night Thoughts; 
Lydia H. Sigourney's Poems ; Mary Howitt's Poems ; Lalla Rookh, by Tom Moore ; 
Montgomery's Poems ; H. Kirke White's Poems ; Lady of the Lake, by Scott ; 
Southey's Poems ; Coleridge's Poems ; Wordsworth's Poems, edited by Prof. Reed ; 
Cowper's Poems; Pollok's Course of Time; Book of Pleasures, Hope, Imagination, 
and Memory ; Thomson's Seasons ; Goldsmith and Gray's Poems ; Elliott's Poems — 
the Corn-law Rhymes; Rogers's Poems; Milton's Paradise Lost; Poetry of the Pas- 
sions; Poetry of the Affections ; Poetry of the Sentiments; Poetry of Flowers; Eliza 
Cook's Poems; Hon. Mrs. Norton's Poems; Byron's Poems; Moore's Poems; 
Burns's Poems. 

These books are printed on good paper, in 32mo size volumes, and beautifully 
bound in various styles. The beauty of the style in which they are got up, with the 
intrinsic merit of their contents, renders them the most valuable series of gift books 
ever issued. There is no one, making any pretence to English literature, but who would 
know something of the authors whose names are given above. 

This is the most beautiful series of gift books published; for that purpose, nothing 
can be so tasteful, and nothing more intrinsically valuable. 

LIBRARY OF FEMALE POETS; containing the works of Mrs. 

Sigourney, Mary Plowitt, Eliza Cook, and Mrs. Norton. Beautifully bound, in a 
uniform style, and done up in neat cases. 

THE ANALYTICAL SPELLING-BOOK. By W. S. Cardell. 

18mo, 144 pp. 

The arrangement of the lessons is good, the choice of words felicitous, and the 
whole rnav be regarded as one of the most successful attempts to supply the junior 
classes with a profitable and truly " Analytical Spelling-Book." Your friend, 

Jos. R. Chandler. 

JACK HALYARD THE SAILOR BOY; or, THE VIRTUOUS 

FAMILY. Designed for American children in families and schools. By W. S. 
Cardell. 18mo, 231 pp. 

This is a book unequalled in its style and moral effect, and as a reading hook in 
schools, unsurpassed in every particular that is essential to such a use. To this, 
hosts of teachers who have used and now use it set their seals. It is extensively used 
in the public and private schools of Philadelphia, as well as in those of different sec- 
tions of the country. The following notice from individuals of high character a3 
teachers, is a high recommendation : — 

We, the subscribers, teachers, have examined, with close attention, the story of 
" Jack Halyard," and feel a pleasure in acknowledging our obligations to the author 
of this interesting work. For the purposes designed, this publication is not, in our 
opinion, surpassed by any one that has fallen under our notice. 

As a work of fiction, probably no other possesses so much of the excellence of truth. 
The characters are portrayed with a master-hand, and, what greatly enhances its prac- 
tical value, their merit is of the imitahle kind. The manner in which it fastens on the 
minds of the young, the varied instruction it conveys, and the love of virtue which it is 
calculated to inspire, with the beautiful simplicity of the style in which its sentiments 
are expressed, render it a work of superior excellence as a class-book in schools. 
Isaac Pierce, Jacob Pierce, Enoch Lewis, 

Simon Barstow, J. Irvine Hitchcock, Seth Smith, 

John H. Wileets, Bishop Davenport, Joseph R. Chandler. 



DAVENPORT'S HISTORY OF THE UNITED STATES. 

containing all the events necessary to be committed to memory ; with the Declaration 
of Independence, the Constitution of the United States, and a Table of Chronology. 

The mode of teaching in this book is by question and answer. All the important 
facts in the history of our country are brought directly before the pupil's eye, by which 
the time and labour of wading through many-chapters of printed matter are saved, and 
the learner introduced to a more thorough knowledge of his subject than by any other 
means. 18mo, 144 pp. 

THE HAPPY FAMILY. By W. S. Cardell, the author of Jack 

Halyard. 

BIOGRAPHY FOR SCHOOLS ; or, GOOD EXAMPLES FOR 

YOUNG PERSONS. By Mrs. Robbins, author of the American Popular Lessons. 

This little book contains a biography of a number of wise and eminent men, written 
in the well-known happy style of the author. While it teaches toread.it also holds up 
for imitation to the youthful mind such examples as the lives of Oberlin, Sir William 
Phipps, Sir Matthew Hale, William Penn, &c, afford. It also contains sketches of 
several prominent female characters. 18mo, 256 pp. 

CHASE'S ARITHMETIC. The Elements of Arithmetic, for schools 

and academies, in which decimal and integral arithmetic are combined, and taught 
inductively, on the system of Pestalozzi. In two parts, 1 & 2. ISmo, 144 & 240 pp. 

This arithmetic is used in some of the New England public schools and in some of the 
private schools of this city. It is pronounced by several distinguished teachers to be 
a far better book than any other now in use. The number of examples is great and 
varied, and the rules clear and explicit. 

RANDOLPH'S ARITHMETIC; or, THE PRACTICAL 

TEACHER ; being an easy and rational introduction to arithmetic, designed for be- 
ginners of every age. 12mo, 192 pp. 

The following is an extract from a notice received from a number of teachers of Balti- 
more : — 

We have examined, with attention, Mr. Randolph's system of arithmetic, and take 
pleasure in stating that, in our estimation, it is grea'ly superior, as an elementary work, 
to any thing of the kind that has fallen under our notice, &.c. 

Recommendation from Philadelphia tear- hers : — 

The undersigned consider Mr. Randolph's Arithmetic one of the best productions of 
the kind which has fallen under their notice. It is what it pretends to be, "An Easy 
and Rational Introduction to Arithmetic." His definitions are clear and determinate. 
His rules are expressed in language so plain as to be intelligible to the youngest learner; 
their application is ample and judicious, and the whole is well calculated to sharpen 
and invigorate the intellect of youth, to lighten the labour of teaching, and render the 
6'udy of this important branch of education pleasant and interesting. 

Though this system is well calculated for general use, yet it seems to be par- 
ticularly adapted to female seminaries, as it affords ample means for overcoming that 
disgust which females too often feel for this study, and for inspiring them with an attach- 
ment for this most useful science. 

R. W. Ccshman, W. E. Ashtox, S. W. Crawford, 

C. B. Trego, William Mann, D. R. Ashton. 

GREEN'S INDUCTIVE GRAMMAR; designed to give young 

pupils a knowledge of the first principles of language, accompanied by progressive 
parsing lessons: the whole intended to inculcate habits of thinking, reasoning, and 
expressing thought. By Richard W. Gkeen. 18mo, 180 pp. 

DAVIS'S MODERN PRACTICAL ENGLISH GRAMMAR, 

adapted to the American system of teaching. 12mo, 175 pp. 

This work is unsurpassed for clearness and conciseness, and adaptation to the wants of 
the present day. 



VALPY'S PALEY'S MORAL AND POLITICAL PHILOSOPHY: 

with questions adapted to the use of schools, by R. W. Green ; to which are added 
notes from popular authors, embracing present opinions in ethical science, and an 
exposition of our own political institutions ; the whole carefully adapted to the use 
of schools of both sexes. 12mo, 298 pp. 

Paley's Moral Philosophy is a standard book. It is found in every gentleman's library, 
and its made use of as a text-book in many of our schools and colleges. It is a treatise 
above all others the best adapted to general use, both on account of its clearness of 
method and aptness of illustration, and also because it contains a code of ethics more 
universal in its application than any other. In the language of an English reviewer, " it 
is a masterly and inimitable work." He had many points of resemblance to Socrates; the 
philosophy of both was common sense, and their study human nature. 

HAZEN'S SPELLER AND DEFINER ; or, CLASS-BOOK 

No. 2, designed to answer the purposes of a Spelling-book, and to supersede the 
necessity of the use of a dictionary as a class-book. By Edward Hazen. 18mo, 215 pp. 
This book is extensively used in both the public and private schools of Philadelphia and 
New York. The sale of it is upwards of 20,000 copies annually. 

GUMMERE'S PROGRESSIVE SPELLING-BOOK ; containing a 

great variety of useful exercises in spelling, pronunciation, and derivation, including 
extensive tables of words deduced from their Greek and Latin roots. In two parts : 
the second part is arranged on the basis of Butter's Etymological Spelling-Book. 
This book presents an exceedingly judicious arrangement of spelling and reading les- 
sons, the latter being composed of the words of the former, thus teaching their use and 
signification. The second part of the work is an etymological dictionary, giving the 
derivation of words from their Greek and Latin roots. This is a highly important 
exercise for scholars somewhat advanced, and supplies to some extent the necessity 
of learning the original languages. 12mo, 216 pp. 

THE PROGRESSIVE SPELLING-BOOK, First Part, is intended 

lor beginners, and contains the reading and spelling lessons of the larger book. ISmo, 

126 pp. 

The above books were written by Samuel R. Gummere, for a long time a very 
prominent teacher at Burlington, N. J., and one every way competent, both from expe 
rience as a teacher and acquirements as a scholar, to write such a work. 

THE YOUNG ORATOR ; designed to prevent Dulness and Mo- 
notony in reading and declamation. By the Rev. J. L. Blare. 

SMART'S HORACE. The Works of Horace translated literally 

into English prose, for the use of those who are desirous of acquiring or recovering 

a competent knowledge of the Latin language. By B. C. Smart, A. M., of Cambridge 

College, England. 

This is a very great aid to the Latin scholar, and is almost indispensable to the 
acquisition of a thorough knowledge of translating. " We believe that the examination 
of judicious translations like the present will be of greater service to the learner than 
years of study." 

JACOB'S LATIN READER, First Part, with a Vocabulary and 

English notes, for the use of schools and academies. Edited by George Bancroft. 

Editor's Advertisement. In preparing the second edition of Jacob's Latin Reader, 
the work has undergone a thorough revision ; notes have been added, and many words, 
which had been omiited in the dictionary, are here inserted in their respective places. 
The editor, in publishing this work in America, was influenced by a belief, that it forms 
an easy introduction to the language and character of the Roman world. He selected 
it as the best from many similar works, and is happy in finding his judgment confirmed 
by that of many instructors. Geokge Bancroft. 

Jacob's Latin Reader is a standard work, and the fact that almost every new Latin 
Reader that has been issued since its publication has been but an adaptation of the edi- 
tor's notes or whims to Jacob's text, proves it to be a super-excellent book. We be- 
lieve no Latin Reader, but that of Jacob under some one or other of its various moui 
fications, is used in the schools of this country. 12uio, 259 pp. 



KINGSLEY'S TACITUS ; containing the five books of History., 

the treatise on the Manners and Customs of the Germans, the life of Julius Agricola 
and the treatise on Oratory: with extensive notes extracted from various sources 
By James L. Kingsley, Professor of the Latin Language in Yale College. 
This book is used in the Boston academies and various classical schools in the country, 

CORNELIUS NEPOS, for the use of classical schools and 

academies. 12mo, 192 pp. 

This is a very neat edition of this author, being beautifully printed and well bound. 
It should be one of the first reading books of all classical students. 

" Cornelius Nepos is, more than any other Roman writer, suited to be put into the 
hands of boys, who have made sufficient progress to be able to read a Roman author 
in course. The simplicity and classical character of his style ; the separate lives, full 
of interest, and not long enough to weary ; the extent of history, of which he gived a 
pleasing outline, by presenting, as in a gallery, those illustrious men who directed the 
fortunes of antiquity ; the general purity of the moral tendencies of his writings, and the 
favourable moral influence which always follows from the true history of great men, 
are circumstances which explain why he is so universally adopted in the European 
schools, and is beginning to be introduced in so many of our own." 

THE NEW LATIN TUTOR; or, EXERCISES IN ETYMO- 
LOGY, SYNTAX, AND PROSODY: compiled chiefly from the best English 
works. By Frederick P. Leverett, Principal of the Public Latin School in Boston. 
12mo, 350 pp. 

AINSWORTH'S LATIN DICTIONARY. 8vo, 1028 pp. 

This work is so well known as hardly to need a notice. Its almost universal use 
in the schools and colleges of this country, as well as in those of England, is an evi- 
dence of its superiority over other works of the kind. It is now offered at a price 
much lower than formerly, while it is manufactured in a superior manner. 

ANTHON'S ABRIDGMENT OF AINSWORTH'S LATIN DIC- 

TIONARY, for the use of grammar-schools. Into this edition are introduced several 
alterations and improvements, for the special purpose of facilitating the labour and in- 
creasing the knowledge of the young scholar. By Charles Anthon, Professor 
of Languages in Columbia College, N. Y. 18mo, 761 pp. 

This work contains about the same number of words as the larger work, the chief 
abridgment being in the quotations and illustrations of the original work. From the 
ronvenience of its size and cheapness, it is particularly adapted (or the use of beginners. 

THE STATE-BOOK OF PENNSYLVANIA; comprising an 

account of its History, Geography, Resources, Leading Incidents, and Prominent 
Men ; illustrated with a Map of the state, and a Map of each county ; intended for the 
use of schools and families. By Thomas H. Burkowes, formerly Secretary of State 
and Superintendent of Public Schools. 12mo, 314 pp. 

This work is intended more particularly to be used as a recitation or reading book in 
the public and private schools of the state. It embraces an account of the climate, 
soil, produciions, manufactures, geology, mineralogy, government, &c, of Pennsylvania, 
arranged in paragraphs, and accompanied with questions for examination. It is such 
a book as every Pennsylvania]! should possess. The pupils of our common schools 
could have no subject of greater interest and practical value presented to them, while 
in this volume it is presented in a style attractive and pleasing. We wish that teachers 
would do us the favour to examine the book. 

THE AMERICAN SYSTEM OF PENMANSHIP. By George 

J. Becker, Professor of Writing in the Philadelphia Central High-school. In Ten 

Numbers. 

In these books the exercises progress in a regular series of advancement, from the 
first rudiments of writing to perfect specimens of penmanship. The copies are printed 
by the Lithographic process, and have every appearance of being executed with a pen, 
thus affording an itnitable copy for the learner. 7'he use of these books will abridge 
the labour of the teacher, and make better writers in half the time usually taken. 

THE INTRODUCTION TO THE ENGLISH READER. By 

L. Murray. A very neat and cheap edition. 

THE ENGLISH READER. By Lindley Murray. A very neat 

and cheap edition. 



GUMMERE'S SURVEYING. A Treatise on Surveying, contain- 
ing the Theory and Practice: to which is prefixed a perspicuous system of Plane 
Trigonometry. The whole clearly demonstrated and illustrated by a large number 
of appropriate examples, particularly adapted to the use of schools. By John 
Gummere, A. M. This is the Standard Treatise on this science now in use in 
this country ; and as a clear, practical exposition, is unequalled by any other work 
on the subject. 

KEY TO GUMMERE'S TREATISE ON SURVEYING. 
BONNYCASTLE'S MENSURATION. An Introduction to Men- 

suration and Practical Geometry, by John Bonnycastle : to which are added a 
Treatise on Gauging, and also the most important Proble.ms in Mechanics, by 
James Ryan. This work, is the chief text-book upon this science now in use. 

KEY TO BONNYCASTLE'S MENSURATION. 

GRtECA MAJORA. 2 vols. 8vo. This work is particularly re- 
commended to the higher Greek classes, as it is the only medium through which 
extracts from the principal Greek authors can be obtained. The first volume is 
devoted to Prose, the second to Verse. The following is a list of some of the 
authors, from whose works copious extracts are given : Herodotus, Thucydides, 
Xenophon, Lysias, Isocrates, Demosthenes, Plato, Aristotle, Dionysius, Halicar- 
nassus, Longinus, Theophrastus, Polyaenus, JElianus, Polybio, Homer, Hesiod, 
Apollonius of Rhodes, Sophocles, Euripides, Theocritus, Bion, Moschus, &c. &c. 
Also a miscellaneous collection of Hymns, Odes, Paeans, &c. This work thus 
contains within itself a library of Greek Literature, furnished at a small cost, 
which otherwise can hardly be obtained at all. 

COMLY'S PRIMER. 

COMLY'S SPELLING BOOK (Enlarged). A new Spelling Book, 

compiled with a view to render the arts of Spelling and Reading easy and pleasant 
to children. By John Comly. 

COMLY'S GRAMMAR. English Grammar made easy to the 

Teacher and Pupil. By John Comly. The general use of this Grammar in the 
best Schools in the United States, is an evidence of its merits. It is the cheapest, 
and is considered by the most experienced teachers, the best elementary work 
extant. 



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